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Name:_________________ Honors geometry Review #1 for MP3 Exam 1.

Name ________________________________________ Date ___________________ Class __________________

Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor.

Holt McDougal Geometry

Properties and Attributes of Triangles Chapter Test Form B

1. Find AB.

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2. The line y 2x 3 is the perpendicular bisector of MN and intersects MN at ( 6, 9). Find an equation of

HJJJGMN in

point-slope form.

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3. Find m DEY.

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4. , ,ZX ZY and ZW are the perpendicular bisectors of TUV. Find XT, VU, and ZV.

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5. GX and XJ are angle bisectors of GHJ. Find m HJX and the distance

from X to GH .

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6. If MX 21.6, find LZ and MW.

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7. Find the coordinates of the orthocenter of the triangle.

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8. Find the perimeter of ABC.

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Properties and Attributes of Triangles Chapter Test Form A continued

10. Write True or False. In an indirect proof, you always assume that the opposite (or negation) of the conclusion is true.

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11. Write True or False. The measures 10, 12, and 16 can be the side lengths of a triangle.

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Use the figures for Exercises 12 and 13.

12. Write the sides of FED in order from smallest to largest.

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13. Compare FD and GJ.

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14. Find the value of x.

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15. Write True or False. A right triangle has sides that measure 5, 12, and 13. The side lengths form a Pythagorean triple.

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16. The measures of the side lengths of a triangle are 3, 4, and 5. Classify the triangle as acute, right, or obtuse.

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17. Find the value of x.

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18. Find the values of x and y.

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2. Explain why the triangles are similar and find DE.

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Practice B Triangle Similarity: AA, SSS, SAS

For Exercises 1 and 2, explain why the triangles are similar and write a similarity statement. 1.

2.

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For Exercises 3 and 4, verify that the triangles are similar. Explain why. 3. UJLK and UJMN 4. UPQR and UUTS

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For Exercise 5, explain why the triangles are similar and find the stated length.

5. DE

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LESSON

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LESSON

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3. Explain why the triangles are similar and find BC

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Reteach Triangle Similarity: AA, SSS, and SAS

Explain how you know the triangles are similar, and write a similarity statement. 1.

2.

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3. Verify that UABC UMNP.

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Angle-Angle (AA) Similarity

If two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar.

UABC UDEF

Side-Side-Side (SSS) Similarity

If the three sides of one triangle are proportional to the three corresponding sides of another triangle, then the triangles are similar.

UABC UDEF

Side-Angle-Side (SAS) Similarity

If two sides of one triangle are proportional to two sides of another triangle and their included angles are congruent, then the triangles are similar.

UABC UDEF

Name ________________________________________ Date ___________________ Class __________________



Reteach Triangle Similarity: AA, SSS, and SAS continued

You can use AA Similarity, SSS Similarity, and SAS Similarity to solve problems. First, prove that the triangles are similar. Then use the properties of similarity to find missing measures.

Explain why UADE UABC and then find BC. Step 1 Prove that the triangles are similar. A A by the Reflexive Property of .

3 16 2

ADAB

2 14 2

AEAC

Therefore, UADE UABC by SAS . Step 2 Find BC.

AD DEAB BC

Corresponding sides are proportional.

3 3.56 BC

Substitute 3 for AD, 6 for AB, and 3.5 for DE.

3(BC) 6(3.5) Cross Products Property 3(BC) 21 Simplify. BC 7 Divide both sides by 3.

Explain why the triangles are similar and then find each length.

4. GK 5. US

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LESSON

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LESSON

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4. Find DE.

5.

Determine whether ΔABC and ΔDEF are similar. If so, write the similarity ratio and a similarity statement.

6.

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Foundations for Geometry Chapter Test Form C continued

10. The measure of A is twice the measure of its complement. What is the measure of A? F 20 H 60 G 30 J 90

11. If m B (180 x) , what is the measure of a supplement of B?

A 180 C (180 x)

B x D (90 x)

12. What is the length of a rectangle if the perimeter is 88 inches and the length is 2 inches more than the width? F 21 in. H 25 in. G 23 in. J 42 in.

13. What is the height of a triangle with an area of 16.5 square meters if the base is 5.5 meters? A 1.5 m C 6 m2 B 3 m D 6 m

14. A circle has an area of 81 square feet. What is its radius? F 9 ft H 20.5 ft G 9 ft2 J 40.5 ft

15. Given GH with endpoints G( 7, 3) and H(7, 11), what are the coordinates of the midpoint of GH ?

A (0, 4) C ( 7, 7)

B (0, 8) D ( 14, 14)

16. M is the midpoint of .RS R has coordinates ( 2, 10), and M has coordinates (3, 5). What are the coordinates of S? F (1, 15) H (8, 0)

G (0.5, 7.5) J (5, 5)

17. What is the distance from M(9, 4) to N( 1, 2)?

A 10 C 2 26

B 10 D 12

18. Given a right triangle with the length of one leg equal to 9 centimeters and the length of the hypotenuse equal to 15 centimeters, what is the length of the other leg?

F 6 cm H 306 cm

G 12 cm J 144 cm

19. What transformation is shown?

A rotation C translation B reflection D image

20. A triangle has vertices A( 3, 6), B(1, 5), and C(2, 4). After a transformation, the image of the triangle has vertices A ( 3, 6), B (1, 5), and C (2, 4). Identify the transformation. F reflection across the x-axis G reflection across the y-axis H rotation J translation

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Triangle Congruence Chapter Test Form C

Circle the best answer. 1. Describe the transformation M: (x, y) (-y, x).

A A reflection across the y-axis. B A reflection across the x-axis. C A rotation 90 clockwise with center

of rotation (0, 0). D A rotation 90 counterclockwise with

center of rotation (0, 0). 2. Which best describes ABC with vertices

A( 2, 1), B(0, 4), and C(2, 1)? F acute H obtuse G equiangular J right

3. Which is a correct classification of DEF with vertices D( 3, 2), E( 2, 3), and F(1, 0)? A equilateral C scalene B isosceles D Not here

4. What is the value of x?

F 41 H 99 G 58 J 122

5. QRS STQ, QS x2 10 and SQ 2x 2. What is the value of x? A 4 C 2 B 2 D 4

6. ABC DEF. What information is NOT needed to find the perimeter of ABC if you are given all four lengths below?

F DE H CF G BG J EF

Use the partially completed two-column proof for Exercise 7. Given:

Prove: GHF MOL

Proof:

Statements Reasons

1. ,

,

GF ML

FH LO

GH MO

1. Given

2. F L 2. ?

3. H O 3. Given

4. G M 4. ?

5. GHF MOL 5. ?

7. Which reason does NOT belong in the proof? A Def. of s B Third s Thm. C Rt. Thm. D CPCTC

Use the figure for Exercises 8–11.

8. AB y 3, DC 3y 1, EB 3y 1, ED y 1, AE y, CE 2y. What value of y proves

AEB CED by the SSS Postulate? F 2 H 1 G 1 J 2

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Triangle Congruence Chapter Test Form B continued

11. If B and C are right angles, what additional congruence statement would allow you to prove DCB ABC by the ASA postulate? A DBC ACB B BDC CAB

C AB DC

D AC DB 12. If A and C are right angles and

AD BC , what postulate or theorem justifies the congruence statement BCD DAB?

F SAS H AAS G ASA J HL

13. A right triangle with leg lengths of 4 and 3 units has to be positioned in the coordinate plane to write a coordinate proof. Which set of coordinates would make the proof easier to complete? A (4, 0), (0, 0), (4, 3) B (3, 0), (0, 0), ( 4, 0) C (0, 4), (0, 0), ( 3, 0) D (0, 4), (0, 0), (3, 0)

14. Which of the following would you find most useful in giving a coordinate proof that two triangles are congruent by SSS? F Distance Formula G Midpoint Formula H CPCTC J Slope Formula


A 12 C 18 B 19.5 D 60

Use the partially completed two-column proof for Exercises 16–18.

Given: GJ bisects FGH, FG HG

Prove: FJ HJ Proof:

16. Which reason belongs in Step 4? F Isosc. Thm. G Conv. of Isosc. Thm. H ASA J Def. of bisector

17. Which reason belongs in Step 5? A Isosc. Thm. C CPCTC B ASA D HL

18. Which reason belongs in Step 6? F Isosc. Thm. G ASA H CPCTC J Def. of bisector

Statements Reasons

1. GJ bisects FGH. 1. Given

2. FGJ HGJ 2. Def. of bisector

3. FG HG 3. Given

4. F H 4. ?

5. FGJ HGJ 5. ?

6. FJ HJ 6. ?

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8.Draw your own diagram

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Foundations for Geometry Chapter Test Form C continued

12. Find the area of a rectangle with a length of x 3 meters and a width of 2x meters. Express your answer in terms of x.

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13. The area of a triangle is 8.25 square centimeters. If the base of the triangle is 3 centimeters, what is the height?

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14. Find the radius of a circle with a circumference of 100 inches.

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15. Find the coordinates of the midpoint of GH with endpoints G(3a, 3a) and H( a, 7a).

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16. M bisects .RS R has coordinates ( 2, 3), and M has coordinates (1, 0). Find the coordinates of S.

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17. AB has endpoints A( 6, 4) and B( 1, 8). CD has endpoints C(2, 5) and D(14, 0). Determine whether the two segments are congruent.

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18. A ladder is leaning against a building. The distance from the building to the bottom of the ladder is 7 feet. The ladder is 25 feet long. How high up the building is the top of the ladder?

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19. Identify the transformation.

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20. A transformation maps E onto F and G onto H. Identify the preimage of H.

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9. WXYZ is a rhombus. What is m∠XYZ and

m∠YZW

10.

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Parallel and Perpendicular Lines Chapter Test Form C continued

10. If a transversal is perpendicular to one of two parallel lines, which statement is NOT correct? F All the angles formed are congruent. G Every pair of angles is supplementary. H The transversal is to the other line. J Every pair of angles is complementary.

11. Which is a possible value of x?

A 21 C 25 B 23 D 26

Use the figure and the partially completed proof for Exercises 12 and 13.

Given: AC is the shortest segment from A to CD and m 1 m 2.

Prove: HJJG HJJGAB AC

Proof: Statements Reasons

1. m 1 m 2 1. Given

2. ___?___ 2. Given

3. AC CDHJJG HJJG

3. Distance from a point to a line

4. ? 4. Conv. of Alternate

Int. s/ Thm.

5. HJJG HJJGAB AC 5. ?

12. Which is the statement for Step 2?

F ||HJJG HJJGAB CD H

HJJG HJJGAC CD

G HJJG HJJGBD CD J Not here

13. Which is the justification for Step 5? A 2 lines to same line 2 lines B 2 intersecting lines form linear pair of

lines C Transv. Thm. D Same-Side Interior Angles Theorem

14. Given the point J( 2, 4), for which point K is

HJJGJK a line with undefined slope?

F K(2, 4) H K(4, 2) G K(2, 4) J K( 2, 4)

15. If EF GH for the points E( 2, 5), F(x, y), G( 2, 2), and H(0, 0), which is a possible ordered pair for F? A (2, 1) C (3, 1) B ( 1, 4) D (3, 10)

16. Given points A( 1, 4), B(0, 4), C(2, 0), and D(2, 5), what type of lines are

HJJGAB

and HJJGCD ?

F parallel H horizontal G perpendicular J vertical

17. Which is an equation of a horizontal line? A x 3 C y x B y 4 D y x

18. Which is the equation of a line that does NOT go through the origin? F x 0 H y x G y x 1 J y 2x

19. Which line is NOT parallel to y x2 23

?

A 2x 3y 6 C 6y 12 4x

B y x1 1 12 3

D 4x 6y 12

20. Which of the following is the equation of the line that passes through (2, 1) and is perpendicular to 5x y 9? F x 5y 3 H x 5y 3

G 355

y x J 355

y x

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11.

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Similarity Chapter Test Form A

Circle the best answer. 1. Which ratio is the slope of the line?

A 13

B 31


23 12

x

A 8 B 18

3. If 4x 3y, which shows the ratio of x to y in simplest form?

A 43

B 34

4. A student made a model of a building. The model was 3 feet high and 12 feet wide. The building is 720 feet wide. Which proportion correctly shows how to find the height of the building?

A 3 12720 x

B 12 3 720

x

C 312 720

x

5. Which similarity statement is true for the triangles shown?

A UABC UDEF B UABC UFED

6. Which value of x make the two rectangles similar?

A 42 B 63 C 84

7. Which similarity postulate or theorem lets you conclude that UJKL UMNO?

A AA B SSS

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12.

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Polygons and Quadrilaterals Chapter Test Form A

Circle the best answer. 1. Which term does NOT describe the

figure?

A concave C polygon B hexagon D regular

2. What is the sum of the measures of the interior angles of a 5-sided convex polygon? A 72 C 540 B 360 D 900

3. What is the value of a?

A 60 B 80

4. The diagonals of .ABCD intersect at X. Which is NOT true? A DAB BCD B m DAB m CBA 180

C BC AD

D AX XB

Use the figure for Exercises 5 and 6.

5. WXYZ is a parallelogram. Which is m W? A 68 B 112

6. WXYZ is a parallelogram. What is the value of x? A 7 B 10

7. Which MUST be a parallelogram?

A Figure 1 B Figure 2

8. If ||EF GH , what additional information would allow you to conclude that EFGH is a parallelogram?

A EF GH

B FG EH

9. Which is NOT always true? A A square is a rhombus. B A rectangle is a parallelogram. C A rhombus is a rectangle. D A square is a rectangle.

10. PQRS is a rectangle. PR 26. What is the value of x?

A 6.5 B 13

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13. Baldwin St. in Duendin, New Zealand, is the steepest street in the world. It has a grade of 38%. To the nearest degree, what angle does Baldwin St. make with the horizontal line? 14. A ramp has a 7% grade. The ramp is 42 ft. long. Find the vertical distance that the ramp rises. Round your answer to the nearest hundredths. 15.A highway exit ramp has a slope of 3/20. To the nearest degree, find the angle that the ramp makes with a horizontal line. 16.

Name ________________________________________ Date ___________________ Class __________________



Foundations for Geometry Section B Quiz

Choose the best answer. 1. What is the perimeter of this rectangle?

A (4x 3) units C (8x 6) units B (4x 34) units

2. To the nearest whole number, what is the area of this circle? Use the A r2.

F 452 in2 H 38 in2 G 113 in2

3. To the nearest tenth, what is the circumference of a circle with a radius of 4 meters? Use C 2 r. A 50.2 m C 12.6 m B 25.1 m

4. Find the coordinates for the midpoint of MN if M( 3, 8) and N( 7, 6). F ( 5, 7) H (2, 1) G (5, 7)

5. K is the midpoint of PQ , P ( 9, 4), and K ( 1, 6). What are the coordinates of Q? A (5, 10) C (7, 16) B ( 11, 8)

6. What is the distance, to the nearest whole number, from K(5, 6) to P(1, 4)?

Use 2 22 1 2 1( ) ( )d x x y y .

F 13 G 11 H 6

7. Which best describes the transformation?

A reflection (flip) B rotation (turn) C translation (slide)

8. A figure has vertices at K(5, 5), L(5, 3), M(1, 1). After a transformation, the image of the figure has vertices at K'( 5, 5), L'( 3, 5), and M'( 1, 1). Which best describes the transformation? F reflection (flip) G rotation (turn) H translation (slide)

16

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Foundations for Geometry Chapter Test Form B

Circle the best answer.


1. What is another name for plane P ?

A plane AE C plane BAD

B plane A D plane BAC

2. Which segment is on line n?

F AD H AC

G BC J BE

3. Which is the name of a ray with endpoint A?

A DAJJJG

C CAJJJG

B BCJJJG

D ABJJJG

4. Name the intersection of plane P and line m.

F line n H AC

G point A J AE

5. What is the measure of RT ?

A 5 C 26

B 16 D 40

6. Given LM MP and L, M, and P are collinear, which of the following BEST describes the relationship of L, M, and P ?

F LM MP

G M is the midpoint of .LP

H M bisects .LP

J All of the above


7. Which term describes PMQ?

A obtuse C right

B straight D acute

8. What is m PMN?

F 22 H 68

G 90 J 112

9. Which angles are adjacent and form a linear pair?

A 1 and 2 C 2 and 3

B 3 and 4 D 1 and 5

10. If m A (4x 2) , what is the measure of the complement of A?

F 90 H (178 4x)

G (4x 92) J (88 4x)

Name ________________________________________ Date ___________________ Class __________________



Foundations for Geometry Chapter Test Form A continued

11. If m B x , what is the measure of a supplement of B? A 90 C (90 x) B 180 D (180 x)

12. What is the perimeter of a square with s 8 centimeters? A 32 cm B 64 cm

13. What is the area of a triangle with a base of 6 inches and a height of 3 inches? A 9 in2 B 18 in2

14. What is the approximate area of a circle with a radius of 4 feet? Use 3.14 for . A 12.56 ft2 C 50.24 ft2 B 25.12 ft2 D 200.96 ft2

15. What are the coordinates of the midpoint of GH with endpoints G( 2, 5) and H(4, 1)? A ( 6, 4) C ( 3, 2) B (1, 3) D (2, 6)

16. M is the midpoint of RS and R has coordinates (2, 5). M has coordinates (6, 9). Find the coordinates of S. A (4.5, 6.5) C (4, 4) B (10, 13) D (16, 16)

17. Use the Distance Formula to find VW.

A 5 C 9

B 29 D 25

18. Use the Pythagorean Theorem to find the length of the hypotenuse.

A 10 C 48 B 14 D 100

19. What transformation is shown?

A translation B reflection

20. What rule would you use to translate a figure in the coordinate plane 2 units to the right? A (x, y) (x 2, y) B (x, y) (x, y 2)

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18. Which angle has a cosine of 3

5?

A ∠A B ∠B

19. Find sin B and cos A as a fraction. What conclusion can you make about angle A and B?

20. a) Are triangles A(1, 7), B(2, 8), C(3, 7) and D(2.5, 17.5), E(5, 20), F(7.5, 17.5) congruent? Describe the transformation that supports your answer. b) Prove that triangles F(4, 6), G(5, 7),H(7, 4) and J(1, -4), K(2, -5), L(4, -2) are congruent, using transformation, and describe the transformation to support your answer 21.

Name ________________________________________ Date ___________________ Class __________________



Foundations for Geometry Chapter Test Form B


1. Name a point on line n.

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2. Name a segment on line m.

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3. Name a ray with endpoint C.

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4. Name three collinear points.

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5. F is between E and G, EF x 7, and EG 4x 3. Find FG.

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6. ,LM QP and LM 13.5. Find QP.

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7. m LMP 57 . Classify LMP as acute, right, or obtuse.

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8. Z is in the interior of WXY. m WXZ 40 , and m WXY 110 . Find m ZXY.

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9. Name a pair of adjacent angles that do NOT form a linear pair.

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10. A and B are complementary. m A (5x 2) . Find m B.

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11. A and B are supplementary. m B 121 . Find m A.

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12. Find the area of a square with s 7.6 centimeters.

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13. Find the area of a triangle that has a base of 4 inches and a height of 7.5 inches.

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Name ________________________________________ Date ___________________ Class __________________



Foundations for Geometry Chapter Test Form A continued

Use the figures for Exercises 12–14.

12. Find the perimeter of the square.

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13. Find the area of the triangle.

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14. Find the circumference of the circle. Express your answer in terms of .

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15. Find the coordinates of the midpoint of GH with endpoints G( 5, 4) and H( 5, 8).

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16. M is the midpoint of ,RS and M has coordinates (2, 6). R has coordinates ( 10, 6). Find the coordinates of S.

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17. Use the Distance Formula to find VW.

2 22 1 2 1( ) ( )d x x y y

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18. Use the Pythagorean Theorem to find the length of the hypotenuse.

a2 b2 c2

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19. Identify the transformation as a reflection, a rotation, or a translation.

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20. The coordinates of the endpoints of a segment are A( 2, 3) and B(2, 1). Find the coordinates for the endpoints of the image of AB after the translation (x, y) (x 3, y 2).

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Chapter

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22.

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Foundations for Geometry Chapter Test Form C


1. Name the plane containing line m.

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2. Name a segment that has only one point on line n.

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3. Name a pair of rays on plane P that contain B but do not have B as an endpoint.

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4. Name three coplanar points NOT on plane P .

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5. S is the midpoint of ,RT RS 2x 4, and RT 8x. Find ST.

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6. M bisects ,QP and QP 27.4. Find QM.

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7. m LMP 132 . Classify the angle as acute, right, or obtuse.

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8. XZJJJG

bisects WXY, and m WXZ 65 . Find m WXY.

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9. Name a pair of vertical angles.

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10. An angle measures three times the measure of its supplementary angle. Find the measure of both angles.

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11. An angle measures 10 less than the measure of its complementary angle. Find the measure of both angles.

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Name ________________________________________ Date ___________________ Class __________________



Foundations for Geometry Chapter Test Form B continued

14. Find the circumference of a circle with a diameter of 6 feet. Use 3.14 for .

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15. Find the coordinates of the midpoint of GH with endpoints G( 7, 3) and H(5, 9).

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16. M is the midpoint of ,RS and M has coordinates ( 1, 5). R has coordinates ( 5, 2). Find the coordinates of S.

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17. Use the Distance Formula to find AB.

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18. Use the Pythagorean Theorem to find VW.

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19. Identify the transformation.

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20. A triangle has vertices at A( 2, 3), B(2, 1), and C(1, 0). After a transformation, the image of the triangle has vertices at A ( 2, 3), B (2, 5), and C (1, 6). Identify the transformation.

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Chapter

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23.

Name ________________________________________ Date ___________________ Class __________________



Triangle Congruence Chapter Test Form A

1. The transformation M: (x, y) (0.5x, 0.5y) has been applied to

the polygon KLM. If the point M had coordinates (4, 4), name the coordinates of the image of M.

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2. Is the polygon K(5, 4), L(5, 6), M(7, 6) congruent to the polygon N(4, 3), P(4, 5), Q(6, 5)?

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3. Classify the triangle by its angle measures.

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4. Classify the triangle by its side lengths.

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5. Complete the sentence. All of the angles in an equilateral triangle measure _________.

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6. What is the measure of 1?

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7. Given: GHJ NOP. What is the value of x?

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8. If KLM RST, what is the value of x?

________________________________________ 9. Complete the statement. Two triangles

are congruent if and only if their _______ angles and sides are congruent.

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10. What value of x proves ABC DEF by SAS?

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11. If AB DE , what additional congruence statement is needed to prove ABC

DEF by SSS?

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12. Write True or False. You can use AAS to prove ABE CDE.

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13. What additional congruence statement is needed to prove ABE CDE by HL?

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Chapter

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*Also write the Similarity statement and the reason 24.

Name ________________________________________ Date ___________________ Class __________________



Triangle Congruence Chapter Test Form A

1. The transformation M: (x, y) (0.5x, 0.5y) has been applied to

the polygon KLM. If the point M had coordinates (4, 4), name the coordinates of the image of M.

_________________________________________

2. Is the polygon K(5, 4), L(5, 6), M(7, 6) congruent to the polygon N(4, 3), P(4, 5), Q(6, 5)?

_________________________________________


3. Classify the triangle by its angle measures.

_________________________________________

4. Classify the triangle by its side lengths.

_________________________________________

5. Complete the sentence. All of the angles in an equilateral triangle measure _________.

_________________________________________

6. What is the measure of 1?

_________________________________________

7. Given: GHJ NOP. What is the value of x?

_________________________________________

8. If KLM RST, what is the value of x?

________________________________________ 9. Complete the statement. Two triangles

are congruent if and only if their _______ angles and sides are congruent.

________________________________________


10. What value of x proves ABC DEF by SAS?

________________________________________

11. If AB DE , what additional congruence statement is needed to prove ABC

DEF by SSS?

________________________________________


12. Write True or False. You can use AAS to prove ABE CDE.

________________________________________

13. What additional congruence statement is needed to prove ABE CDE by HL?

________________________________________

Chapter

x

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Chapter

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73


25. a) Given the points A(–1, 2) and B(7, 8), find the coordinates of the point P on directed line segment that partitions in the ratio . Plot P. COORD::

b). TWO:: Find the coordinates of P so that P partitions the segment in the ratio 5:1 if A(2, 4) and B(8, 10). (Sketch this on your own) 26.

Name ________________________________________ Date ___________________ Class __________________



Similarity Chapter Test Form B

Circle the best answer. 1. Which similarity statement is true for

rectangles JKLM and PQRS, given that JK 6, JM 5, QR 15, and PQ 12.5?

A rectangle JKLM rectangle PQRS B rectangle JKLM rectangle QRSP C rectangle JKLM rectangle RQPS D rectangle JKLM rectangle SRQP

2. JKL MNO. The similarity ratio of

JKL to MNO is 52

. What is the length

of MN ?

F 6 G 10.8 H 14 J 37.5

3. An atrium has the dimensions shown. A scale drawing of the atrium is actually 6 cm wide. What is the length of the scale drawing?

A 1.9 cm C 19.2 cm B 3.3 cm D 48 cm

4. Which of the following transformations is NOT a similarity transformation? F M: (x, y) (0.3x, 0.3y) G M: (x, y) (10x, 10y) H M: (x, y) (4x, 2y) J M: (x, y) (0.8x, 0.8y)

5. The dilation D: (x, y) § ·¨ ¸© ¹

3 3, 4 4

x y has

been applied to the polygon S(12, 16), T(–12, –16), U(4, 4). What are the coordinates of the image points? A S'(9, 12), T'( 9 , 12), U'(3, 3) B S'(36, 48), T'( 36, 48), U'(12, 12) C S'(12, 16), T'( 12, 16), U'(4, 4)

D S'(12 3 ,4

16 34

), T'( 11 1 ,4

15 14

),

U'(4 3 ,4

4 34

)

6. Polygon K(1, 0), L(8, 3), M(9, 4), N(2, 1) was mapped to polygon O( 1, 1), P(20, 10), Q(23, 13), R(2, 4). What was the similarity transformation? F translate: (x, y) (x 2, y + 1) G first dilate: (x, y) (3x, 3y) then

translate: (x, y) (x – 4, y + 1) H first translate: (x, y) (x – 3, y + 2)

then dilate: (x, y) (0.5x, 0.5y) J translate: (x, y) (x + 0, y + 3)

7. Which similarity postulate or theorem lets you conclude that ABC CDE?

A AA B SAS C SSS D Triangles not similar

Name ________________________________________ Date ___________________ Class __________________



Similarity Chapter Test Form A continued

8. What is the length of AC ?

A 10

B 12

C 15

D 20

9. HJJG HJJG

|| .TS PR What is the length of QS ?

A 15

B 20

C 22

D 24

10. Which proportion is correct?

A JX XHGH GJ

B JX GJXH GH

11. If you are using indirect measurement, what is true?

A You must convert dimensions to the same unit of measurement.

B You do not have to convert dimensions to the same unit of measurement.

12. The scale on a map is 1.5 cm : 1280 m. If the distance between the school and the library on the map is 12 centimeters, what is the actual distance between the buildings?

A 15 m

B 150 m

C 9600 m

D 10,240 m

13. Which coordinates for V make SOT UOV?

A (0, 6)

B (4, 0)

C (6, 0)

D (8, 0)

14. ABC has vertices A(0, 0), B(0, 6), and C(4, 0). Which set of coordinates can be used to prove ABC DEF?

A D(0, 0), E(3, 0), F(0, 2)

B D(0, 0), E(0, 3), F(2, 0)

Chapter

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Chapter

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27.

Name ________________________________________ Date ___________________ Class __________________



Similarity Chapter Test Form C

Circle the best answer. 1. Which similarity statement appears to be

true for the figures shown?

A pentagon AEDCB pentagon NMLKJ B hexagon DCBAE hexagon MLKJN C pentagon DCBAE pentagon KJMNL D pentagon DCBAE pentagon MLKJN

2. What is CD if .ABCD . ?TUVW

F 12 H 42 G 28 J 84

3. A scale drawing of a specialized boxing ring has the dimensions shown. The actual ring has the dimension shown. What is the value of x?

A 0.625 ft C 8.1 ft B 1.6 ft D 10 ft

4. Which of the following transformations is NOT a similarity transformation? F M: (x, y) (3x, 4y) G M: (x, y) (5x, 5y) H M: (x, y) (0.01x, 0.01y) J M: (x, y) (0.66x, 0.66y)


1 1, 10 10

x y has

been applied to the polygon V(–6, 4), W(6 , 8), X(–2, –1). What are the coordinates of the image points? A V (60, –40), W (–60, –80),

X (20, 10) B V (–60, 40), W (60, 80),

X (–20, –10) C V (0.6, –0.4), W (–0.6, –0.8),

X (0.2, 0.1) D V (–0.6, 0.4), W (0.6, 0.8),

X (–0.2, –0.1)

6. Polygon S(10, –4), T(–8, 4), U(5, 5), V(8,0) was mapped to polygon W(6, –3.5) X(–3, 0.5), Y(3.5, 1), Z(5, –1.5). What was the similarity transformation? F translate: (x, y) (x – 4, y – 0.5) G translate: (x, y) (x – 3, y – 1.5) H first translate: (x, y) (x 2, y – 3)

then dilate: (x, y) (0.5x, 0.5y) J first dilate: (x, y) (2x, 2y) then

translate: (x, y) (x – 14, y 4.5)

7. Given EK 29

EG and EJ 29

EF, which

similarity postulate or theorem proves EFG EJK?

A AA B SSS C SAS D Not here

Name ________________________________________ Date ___________________ Class __________________



Similarity Chapter Test Form B continued

8. What is ST?

F 18.75 G 20 H 32.5 J 45

9. What information guarantees that XY AC?

A XB 20, BY 25 B XB 24, BY 30 C XB 25, BY 20 D XB 32, BY 40

10. In JKL, the bisector of J divides intoKL XK with length y 3 and XL

with length 2y. If JK 12 and JL 16, which could be the length of XK ? F 6 G 9 H 12 J 16

11. A student who is 60 inches tall measured shadows to find the height of a tree. The student’s shadow was 24 inches long, and the shadow of the tree was 13 feet long. Which proportion should the student use to find the height of the tree in inches?

A 60 24156 x

C 6024 13

x

B 5 213 x

D 6024 156

x

12. A blueprint uses a scale of 1.5 in : 24 ft. If the actual room has a width of 12 yards and a length of 17 yards, how long is the room on the blueprint?

F 34

in.

G 1 116

in.

H 2 14

in.

J 3 316

in.

13. Which are the coordinates of ABC with vertices A(0, 2), B( 2, 2), and C(2, 4)

after a dilation with a scale factor of 32

?

A A (0, 3), B ( 3, 3), and C (3, 6) B A (0, 1.6), B ( 1.6, 1.6), and

C (1.6, 4.8) C A (0, 3), B (3, 3), and C (3, 6) D A (1.5, 3), B ( 3, 3), and C (3, 6)

14. STU has vertices S(1, 2), T(2, 4), and U(6, 2). Which set of coordinates can be used to prove PQR STU? F P(0.5, 1), Q(3, 1), and R(1, 2) G P(1.5, 3), Q(3, 6), and R(9, 1.5) H P(1.5, 3), Q(3, 6), and R(3, 1) J P(2, 4), Q(4, 8), and R(12, 4)

Chapter

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Chapter

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28.

Name ________________________________________ Date ___________________ Class __________________



Similarity Chapter Test Form B

Circle the best answer. 1. Which similarity statement is true for

rectangles JKLM and PQRS, given that JK 6, JM 5, QR 15, and PQ 12.5?

A rectangle JKLM rectangle PQRS B rectangle JKLM rectangle QRSP C rectangle JKLM rectangle RQPS D rectangle JKLM rectangle SRQP

2. JKL MNO. The similarity ratio of

JKL to MNO is 52

. What is the length

of MN ?

F 6 G 10.8 H 14 J 37.5

3. An atrium has the dimensions shown. A scale drawing of the atrium is actually 6 cm wide. What is the length of the scale drawing?

A 1.9 cm C 19.2 cm B 3.3 cm D 48 cm

4. Which of the following transformations is NOT a similarity transformation? F M: (x, y) (0.3x, 0.3y) G M: (x, y) (10x, 10y) H M: (x, y) (4x, 2y) J M: (x, y) (0.8x, 0.8y)


3 3, 4 4

x y has

been applied to the polygon S(12, 16), T(–12, –16), U(4, 4). What are the coordinates of the image points? A S'(9, 12), T'( 9 , 12), U'(3, 3) B S'(36, 48), T'( 36, 48), U'(12, 12) C S'(12, 16), T'( 12, 16), U'(4, 4)

D S'(12 3 ,4

16 34

), T'( 11 1 ,4

15 14

),

U'(4 3 ,4

4 34

)

6. Polygon K(1, 0), L(8, 3), M(9, 4), N(2, 1) was mapped to polygon O( 1, 1), P(20, 10), Q(23, 13), R(2, 4). What was the similarity transformation? F translate: (x, y) (x 2, y + 1) G first dilate: (x, y) (3x, 3y) then

translate: (x, y) (x – 4, y + 1) H first translate: (x, y) (x – 3, y + 2)

then dilate: (x, y) (0.5x, 0.5y) J translate: (x, y) (x + 0, y + 3)

7. Which similarity postulate or theorem lets you conclude that ABC CDE?

A AA B SAS C SSS D Triangles not similar

Name ________________________________________ Date ___________________ Class __________________



Similarity Chapter Test Form A continued

8. What is the length of AC ?

A 10

B 12

C 15

D 20

9. HJJG HJJG

|| .TS PR What is the length of QS ?

A 15

B 20

C 22

D 24

10. Which proportion is correct?

A JX XHGH GJ

B JX GJXH GH

11. If you are using indirect measurement, what is true?

A You must convert dimensions to the same unit of measurement.

B You do not have to convert dimensions to the same unit of measurement.

12. The scale on a map is 1.5 cm : 1280 m. If the distance between the school and the library on the map is 12 centimeters, what is the actual distance between the buildings?

A 15 m

B 150 m

C 9600 m

D 10,240 m

13. Which coordinates for V make SOT UOV?

A (0, 6)

B (4, 0)

C (6, 0)

D (8, 0)

14. ABC has vertices A(0, 0), B(0, 6), and C(4, 0). Which set of coordinates can be used to prove ABC DEF?

A D(0, 0), E(3, 0), F(0, 2)

B D(0, 0), E(0, 3), F(2, 0)

Chapter

x

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Chapter

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29.

Name ________________________________________ Date ___________________ Class __________________



Polygons and Quadrilaterals Chapter Test Form C continued

10. Find the perimeter of a square if half of a diagonal is equal to 8 inches.

_________________________________________

11. Determine the value of x.

_________________________________________

12. Write True or False. If the midpoints of the sides of a parallelogram, when connected in order, form a rectangle, then the parallelogram is a rhombus.

_________________________________________

13. Use the diagonals to determine whether a parallelogram with vertices ( 3, 2), ( 1, 4), (8, 5), and (6, 7) is a rectangle, rhombus, or square.

_________________________________________

14. Give the best name for the quadrilateral with vertices ( 1, 1), (1, 3), (3, 1), and (1, 3).

________________________________________

15. Find the value of x so that ABCD is an isosceles trapezoid with bases AD and BC .

________________________________________

16. XY is the midsegment of the trapezoid. Find the value of x.

________________________________________

Chapter

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Chapter

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118


30.

31. Find the scale factor

32.

33.

Name ________________________________________ Date ___________________ Class __________________



Properties and Attributes of Triangles Chapter Test Form C

Circle the best answer. 1. AC is the perpendicular bisector of .BD

What is the value of x?

A 2.4 C 263

B 4 D Not here

2. Which is the equation of the line that is the perpendicular bisector of the segment with endpoints (n, 5) and (n, 3)? F y 1 H x 4 G y 4 J y n

3. What is m XYZ?

A 70 C 145 B 125 D Not here

4. Which is the center of the circumscribed circle for the triangle with vertices at (0, 0), (0, 8), and (8, 4)? F (3, 4) H (4, 6) G (4, 3) J (8, 4)

5. Which is the radius of a circle inscribed in KLM?

A the distance from the incenter to a side of the triangle

B the distance from the circumcenter to a side of the triangle

C the distance from the incenter to a vertex of the triangle

D the distance from the circumcenter to a vertex of the triangle

6. If (2, 4) is the location of the centroid of a triangle, which CANNOT be the coordinates of the vertices of the triangle? F (0, 0), (0, 6), (6, 6) G (3, 4), (3, 2), (0, 6) H (3, 2), (1, 6), (2, 8) J (2, 0), (1, 8), (3, 4)

7. Which are the coordinates of the vertices of a triangle with orthocenter ( 4, 3)? A (4, 1), ( 2, 5), (6, 5) B ( 1, 0), ( 1, 5), ( 5, 3) C ( 2, 0), ( 2, 5), ( 5, 3) D ( 4, 0), ( 1, 5), ( 5, 5)

8. ABC is the midsegment triangle of TUV. Which measure CANNOT be

determined?

F m VAC H m CBT G m TAC J m AVC

9. PQ is the midsegment of GHK, and GH is the midsegment of KLM. What is the length of PK ?

A 4 C 14 B 7 D 28

Name ________________________________________ Date ___________________ Class __________________



Properties and Attributes of Triangles Chapter Test Form B continued

9. TUV is the midsegment triangle of ABC. Which angle does NOT

necessarily measure 40 ?

A VTU C CTV B TUA D VBU

10. Which statement is used in an indirect proof to show that an equiangular triangle cannot have a right angle? F Isosc. Thm. G Sum Thm. H Rt. Thm. J Acute of a rt. are

complementary.

11. The lengths of two sides of a triangle are 7 and 11. Which could NOT be the length of the third side? A 5 C 12 B 10 D 19

12. Which statement is false?

F KLM is scalene. G ML KM KL H m L m K J KM ML

13. Which best describes the range of values for x?

A 0 x 7 C x 15 B 0 x 15 D 6 x 7

14. What is the value of x in simplest radical form?

F 3 12 H 72

G 6 2 J 89

15. Which numbers form a Pythagorean triple?

A 3, 4, 6 C 9, 12, 15

B 7, 6 2, 11 D 8, 15, 18

16. Which side length will form an obtuse triangle with sides of length 8 and 10?

F 6 H 12

G 9 J 13

17. What is the value of x in simplest radical form?

A 2.5 C 5 2

2

B 52

D 5 2

18. Which is a correct set of values?

F x 27, 9 3,y 18 3z

G x 27, 18 3,y 9 3z

H 9 3,x y 27, 18 3z

J 18 3,x 9 3,y z 27

Chapter

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Chapter

5

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34. Given: ∠A ≅ ∠D, ∠B ≅ ∠E, ∠C ≅ ∠F, ≅ ,AB DE ≅ ,BC EF and .CA FD≅ Which is a correct congruence statement? A ΔBCA ≅ ΔDEF B ΔABC ≅ ΔDEF

34.

Name ________________________________________ Date ___________________ Class __________________



Triangle Congruence Chapter Test Form B

Circle the best answer. 1. Describe the transformation M:

(x, y) (-x, -y). A A translation one unit down and one

unit to the right. B A reflection across the x-axis. C A rotation 180 with center of rotation

(0, 0). D A dilation with a scale factor -1 and

center (0, 0). 2. Classify the triangle.

F isosceles acute G isosceles obtuse H scalene acute J scalene obtuse

3. What is the length of side BC ?

A 3 C 10 B 8 D 24


4. What is m KLM? F 3 H 42 G 22 J 64

5. What is m M? A 0.2 C 26 B 4 D 64

6. What is the m U?

F 5 H 40 G 15 J 120

7. Two congruent triangles have the following corresponding parts:

, ,RS UV RT UW and R U. Which is NOT necessarily a correct congruence statement?

A RST UVW B STR VWU C TRS VWU D TRS WUV

8. KLM RST. m L (3x 15) and m S (6x 3) . What is the value of x? F 2 H 6 G 4 J 27


9. If AD 5y 7 and BC 7y 3, what must the value of y be to prove

AED CEB by the SSS Postulate? A 2 C 17 B 5 D 32

10. What postulate or theorem justifies the congruence statement ABE CDE? F SSS H ASA G SAS J AAS

Name ________________________________________ Date ___________________ Class __________________



Triangle Congruence Chapter Test Form A continued


10. Which postulate or theorem can you use to prove ABE CDE? A SSS B SAS C ASA D AAS

11. What additional information will prove ABE CDE by HL?

A AB CD

B AE CE

12. To write a coordinate proof, you position a right isosceles triangle in the coordinate plane. The legs measure two units. What is the best position for the vertex angle? A (0,0) B (0,2) C (2, 0) D (2, 2)

13. Given: ABCD is a square with vertices A(0,0), B(0, 4), C(4, 4), and D(4,0). In a coordinate proof, what information would be used to prove AB CD if you do NOT use the distance formula? A x-coordinate of A, x-coordinate of C B y-coordinate of A, y-coordinate of C C y-coordinate of A, x-coordinate of C D x-coordinate of A, y-coordinate of C


A 22.5 B 30 C 45 D 60


15. What postulate or theorem proves ?HG FG

A Isosceles Triangle Theorem B Converse of Isosceles Triangle

Theorem

16. If FGJ HGJ, what reason justifies the statement HGJ FGJ? A ASA B Reflex. Prop. of C Def. of bisects D CPCTC

Chapter

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CS10_G_MEAR710334_C04MCCT.indd 68 4/5/11 6:14:13 PM

35-‐36

Name ________________________________________ Date ___________________ Class __________________



Parallel and Perpendicular Lines Chapter Test Form B



1. Classify EH and .DH

A skew segments

B parallel segments

C perpendicular segments

D parallel planes

2. How many segments are skew to AE ?

F 1 H 3

G 2 J 4


3. Which are alternate exterior angles?

A 1 and 3 C 3 and 6

B 1 and 8 D 6 and 7

4. Which statement is true?

F 1 and 2 are alternate interior angles.

G 1 and 3 are corresponding angles.

H 3 and 6 are alternate exterior

angles.

J 3 and 7 are same-side interior

angles.

5. Which correctly completes the sentence?

If two parallel lines are cut by a transversal,

then the two pairs of same-side interior

angles are _________.

A supplementary

B complementary

C corresponding

D congruent

6. What type of angle is 1?

F acute H obtuse

G right J straight

7. Given ,HJJG HJJGRS QP|| what is the value of x?

A 6 C 72

B 9 D 108


8. Which information proves that r || s?

F 1 3 H 4 6

G 4 5 J 5 6

9. If m 3 (4x 20) and

m 5 (6x 10) , what value

of x proves that r || s?

A 5 C 40

B 15 D 100

10. If a transversal is perpendicular to one of

two parallel lines, how many different

angle measures are formed?

F 1 H 4

G 3 J 8

Name ________________________________________ Date ___________________ Class __________________



Parallel and Perpendicular Lines Chapter Test Form A continued

11. Which segment’s length gives the distance from G to line ?

A GF B GE

12. Which inequality is correct?

A x 23 B x 20

13. If 1 2 and 4 is a right angle, which postulate or theorem is used to prove m || n?

A Alt. Int. Thm. B 2 lines to same line 2 lines are || C Corr. Post. D Vert. Thm.

14. What type of slope does the line have?

A positive C zero B negative D undefined

15. What is the slope of the line through (3, 6) and (4, 2)?

A 4 C 87

B 14

D 4

16. Given a line with a slope of 2, what is the slope of a line parallel to the given line?

A 2 C 12

B 12

D 2

17. Which equation is in slope-intercept form?

A 2 93

y x

B 22 ( 6)3

y x

18. A line parallel to the x-axis could contain which point? A (0, 2) B (2, 0)

19. Which line is perpendicular to y 2x 4?

A y 2x 6 B 1 72

y x

20. What is the equation of the line through ( 1, 8) and (4, 18)?

A 1 102

y x C y 2x 10

B x 2y 10 D 2x y 10

Chapter

x

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Chapter

3

49


37.

Name ________________________________________ Date ___________________ Class __________________



Foundations for Geometry Section A Quiz

Choose the best answer. Refer to the figure for Exercises 1 and 2.

1. Which represents the name of the ray

whose endpoint is K and that passes through R?

A RKHJJG

C KSJJJG

B KTJJJG

D RKJJJG

2. In the diagram, how many different rays have endpoint R?

F 1 H 3

G 2 J 4

Refer to the figure for Exercises 3 and 4.

3. Which line contains points S and U?

A line m C line p

B line n D STHJJG

4. In the diagram, how many different segments can be named?

F 0 H 2

G 1 J 3

Refer to the figure for Exercises 5 and 6.

5. What is MP?

A 1 C 4

B 2 D 5

6. What is LP?

F 7.5 H 2.5

G 2.5 J 7.5

7. What is the first step in constructing a segment congruent to KL ?

A Measure KL . C Estimate KL.

B Draw a line D Swing an arc with a straight with compass edge. point on K.

8. B is the midpoint of AC AB 8v, and AC 2v 42. What is BC?

F 24 H 56

G 48 J 168

9. An angle whose measure is 70 is what type of angle?

A acute C obtuse

B right D straight

10. GJJJJG

bisects FGH, m FGJ (7x 9) , and m HGJ (2x 36) . What is m FGH?

F 43 H 86

G 54 J 108

11. An angle measuring 22 is bisected. What is the measure of the angles that are formed?

A 11 C 33

B 22 D 44

12. Which angle forms a linear pair with MPS?

F RPN H MPJ G RPM J MPK

13. If m Q (8x 40) , what is the measure of its supplement?

A (130 8x) C 90

B (220 8x) D 180

Chapter

x

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Chapter

1

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CS10_G_MEAR710334_C01QZa.indd 5 405011 11:57:58 AM

Name ________________________________________ Date ___________________ Class __________________



Polygons and Quadrilaterals Section B Quiz

Choose the best answer. 1. Which MUST be a square?

A

C

B

D

2. Which is NOT necessarily a rhombus?

F H

G J

3. PQRS is a rectangle. Find ST.

A 10 C 12.5 B 12 D 25

4. Quadrilateral RSTU is a parallelogram. What other information would allow you to prove that RSTU is a rectangle? F Opposite angles are congruent. G Opposite sides are congruent. H The diagonals bisect the angles. J The diagonals are congruent.

5. WXYZ is a rhombus. What is m XYZ?

A 100 C 140 B 120 D 160

6. KLMN is a square and LN NP .

Which can be proved? F KPN KQN

G ||PN KM

H KQ PN

J KP 12

LN

7. A certain kite has exactly one acute angle, and it measures 16 . What is the maximum whole-number measure of the angle opposite that angle? A 74 C 106 B 90 D 164

8. Three sides of a kite measure 8 inches, 10 inches, and 8 inches. What is the perimeter of the kite? F 26 in. H 34 in. G 28 in. J 36 in.

9. A trapezoid midsegment measures 6. One of the bases measures 10. What is the measure of the other base? A 2 C 14 B 8 D 16

Chapter

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Chapter

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CS10_G_MEAR710334_C06QZb.indd 106 405011 12:21:24 PM

38.

39. Which line is parallel to = +y x1 52

?

A 2y = x + 7 C 2y = x + 10

B y = −2x + 5 D y = 2x + 10 40. Which line coincides with y = 4x + 2?

F y = 4x − 2 H y = −4x + 2 G 4y = x + 8 J 8x − 2y = −4

Name ________________________________________ Date ___________________ Class __________________



Parallel and Perpendicular Lines Chapter Test Form B



1. Classify EH and .DH

A skew segments

B parallel segments

C perpendicular segments

D parallel planes

2. How many segments are skew to AE ?

F 1 H 3

G 2 J 4


3. Which are alternate exterior angles?

A 1 and 3 C 3 and 6

B 1 and 8 D 6 and 7

4. Which statement is true?

F 1 and 2 are alternate interior angles.

G 1 and 3 are corresponding angles.

H 3 and 6 are alternate exterior

angles.

J 3 and 7 are same-side interior

angles.

5. Which correctly completes the sentence?

If two parallel lines are cut by a transversal,

then the two pairs of same-side interior

angles are _________.

A supplementary

B complementary

C corresponding

D congruent

6. What type of angle is 1?

F acute H obtuse

G right J straight

7. Given ,HJJG HJJGRS QP|| what is the value of x?

A 6 C 72

B 9 D 108


8. Which information proves that r || s?

F 1 3 H 4 6

G 4 5 J 5 6

9. If m 3 (4x 20) and

m 5 (6x 10) , what value

of x proves that r || s?

A 5 C 40

B 15 D 100

10. If a transversal is perpendicular to one of

two parallel lines, how many different

angle measures are formed?

F 1 H 4

G 3 J 8

Name ________________________________________ Date ___________________ Class __________________



Parallel and Perpendicular Lines Chapter Test Form A continued

11. Which segment’s length gives the distance from G to line ?

A GF B GE

12. Which inequality is correct?

A x 23 B x 20

13. If 1 2 and 4 is a right angle, which postulate or theorem is used to prove m || n?

A Alt. Int. Thm. B 2 lines to same line 2 lines are || C Corr. Post. D Vert. Thm.

14. What type of slope does the line have?

A positive C zero B negative D undefined

15. What is the slope of the line through (3, 6) and (4, 2)?

A 4 C 87

B 14

D 4

16. Given a line with a slope of 2, what is the slope of a line parallel to the given line?

A 2 C 12

B 12

D 2

17. Which equation is in slope-intercept form?

A 2 93

y x

B 22 ( 6)3

y x

18. A line parallel to the x-axis could contain which point? A (0, 2) B (2, 0)

19. Which line is perpendicular to y 2x 4?

A y 2x 6 B 1 72

y x

20. What is the equation of the line through ( 1, 8) and (4, 18)?

A 1 102

y x C y 2x 10

B x 2y 10 D 2x y 10

Chapter

x

48

Chapter

3

48


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