geometry midterm review - quia · geometry midterm review multiple choice identify the choice that...

Name: ______________________ Class: _________________ Date: _________ ID: A

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Geometry Midterm REVIEW

Multiple ChoiceIdentify the choice that best completes the statement or answers the question.

1. Given LM = MP and L, M, and P are not collinear. Draw a picture.A xB xC xD x

2. Given the conditional statement “If it is July, then it is summer in the United States,” write its inverse and give its truth value?F xG xH xJ x

3.

What kind of angles are <2 and <7? Identify the 2 pairs of same-side interior angles.A xB xC xD x

4.

<6= 72 and <3= 106 Can you prove that r Ä s?F xG xH xJ x

5. Which line is perpendicular to y = −13

x + 5?

A y= 3x + 5B y= -3x +5C y = x + 10D y = 2x + 10

6. Are the graphs of the following equations coinciding, intersecting, or parallel? y= 3x + 5 and -3y + 9x =-15F xG xH xJ x

7. Two congruent triangles have the following corresponding parts: RS ≅ UV, RT ≅ UW, and ∠R ≅ ∠U.Is triangle TRS = triangle VWU?A xB xC xD x

8. Is point (-2, 1) on the perpendicular bisector of the segment with endpoints −2,5Ê

ËÁÁˆ̃̃ and

−2,−3ÊËÁÁ

ˆ̃̃? Explain.

F xG xH x J x

9. The lengths of two sides of a triangle are 4 and 9. What is the possible range of the legth measure of the third side?

A xB xC xD x

Name: ______________________ ID: A

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10. What is the measure of <K ? Classify the triangle according to its angles.

F xG xH xJ x

11. If y= 32, what are the values of Z and X ?

A xB xC xD x

Short Answer

1. What is m∠PMN ?

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

3. What is the perimeter of a square whose side is 3.6 inches?

4. Given GH with endpoints G −9, 5ÊËÁÁ

ˆ̃̃ and

H −11, −3ÊËÁÁ

ˆ̃̃, what are the coordinates of the

midpoint of GH ?

5. M is the midpoint of RS. R has the coordinates −6, − 1ÊËÁÁ

ˆ̃̃, and M has coordinates −1,1Ê

ËÁÁˆ̃̃. What

are the coordinates of S?

6. What is the distance from M −1, 8ÊËÁÁ

ˆ̃̃ to

N 10, 4ÊËÁÁ

ˆ̃̃?

7. Given a point in the coordinate plane, the rule x, yÊËÁÁ

ˆ̃̃ → x − 1, y + 4Ê

ËÁÁˆ̃̃translates the point in

which direction?

8. What is the next item in the pattern?2, 4, 16, . . .

9. Write the contrapositive and give its truth value for the conditional statement “If it is the weekend, then it is Saturday”

10. Identify the property that justifies the statement “If ∠B = ∠A and <A = <C, then ∠B = ∠C.”

Name: ______________________ ID: A

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11. Given: ∠2 ≅ ∠3, and ∠1 and ∠2 are adjacent angles whose noncommon sides form a straight line. Prove: ∠1 and ∠3 are supplementary.Complete the Two-Column Proof:

12. Write the conditional statement and converse within the biconditional.Mary can paint the entire living room if and only if she has enough paint.

13. Solve the equation 3 (2x + 1) = 27 . Write a justification for each step.3 (2x + 1) =27 Given equation

6x + 3 =27 [1]6x =24 [2]

x =4 [3]

14. Identify the property that justifies the statement.If AB ≅ CD , then CD ≅ AB

Name: ______________________ ID: A

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15. Use the given flowchart proof to write a two-column proof of the statement AF ≅ FD.

Flowchart proof:AB = CD;BF = FC

AB +BF = AF

FC+CD = FD

GivenSegment Addition Postulate

AB +BF =

FC+CDAF = FD AF ≅ FD

Addition Property of

Equality

Substitution Definition of congruent segments

Complete the proof.

Two-column proof:Statements Reasons

1. AB = CD; BF = FC 1. Given2. [1] 2. Addition Property of Equality3. [2] 3. Segment Addition Postulate4. AF = FD 4. Substitution5. AF ≅ FD 5. Definition of congruent segments

16.

Classify BF and BC.

17. Which correctly completes the sentence?If two parallel lines are cut by a transversal, then the two pairs of corresponding angles are _________.

18. Given: AB→←⎯⎯

Ä CD→←⎯⎯

. E is on AB→←⎯⎯

, and F is on CD→←⎯⎯

.

EF→←⎯⎯

is the perpendicular bisector of CD. What is

the shortest segment from E to CD→←⎯⎯

?

19. Which describes the slope of a vertical line?

20. What is the slope of the line through −12, 8ÊËÁÁ

ˆ̃̃

and 6, − 2ÊËÁÁ

ˆ̃̃?

21. Given points A 2, − 1ÊËÁÁ

ˆ̃̃, B 7, 2Ê

ËÁÁˆ̃̃, C 2, − 3Ê

ËÁÁˆ̃̃, and

D −3, − 6ÊËÁÁ

ˆ̃̃, what type of lines are AB

→←⎯⎯

and CD→←⎯⎯

?

Name: ______________________ ID: A

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22. Describe the transformation M: x, yÊËÁÁ

ˆ̃̃ → y, xÊ

ËÁÁˆ̃̃.

23. Classify the triangle.

24. Triangle ABC is equiangular. AB= 6x +2 and BC= 2x + 18. What is the length of side BC?

25. What is the m∠U?

26. KLM ≅ RST. m∠L = 8x + 9( ) ° and m∠S = 3x + 29( ) °. What is the value of x?

27.

What postulate or theorem justifies the congruence statement ABE ≅ CDE?

28. If ∠A and ∠C are right angles and AD ≅ BC, what postulate or theorem justifies the congruence statement BCD ≅ DAB?

29. Triangle ABC is equilateral. <C= 3x - 6 . What is the value of x?

30. Given: GJ bisects ∠FGH, FG ≅ HG

Prove: FJ ≅ HJProof:

Which reason belongs in Step 6?

31. Point Z is the circumcenter of TUV. What is the value of UV?

Name: ______________________ ID: A

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32. If WX = 7.2, WL = 12.2, and KW = 16, what is the value of ZW?

33. SQ is a midsegment of NOP. What is the

length of OP if SQ= 3x - 1 and OP= 10x - 14?

34. Triangle ABC is a right triangle with hypotenuse 12 and one of the legs 4. What is the lenght of the other leg in simplest radical form?

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

36. Triangle ABC is a 45-45-90 triangle with hypotenuse 7. What is the length of each leg in simplest radical form?

37. Write an equation in point-slope form for the perpendicular bisector of the segment with endpoints A(−2,2) and B(5,4).

38. What is another name for line n? What is another name for plane P ?

39. S is in between segment RT. RS= 20, ST= 3x + 4, and RT= 9x. What is the measure of RT ?

ID: A

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Geometry Midterm REVIEWAnswer Section

MULTIPLE CHOICE

1. ANS: D PTS: 1 DIF: Average TOP: Chapter 1 Multiple Choice Test, Form B DOK: DOK 2

2. ANS: H PTS: 1 DIF: Average TOP: Chapter 2 Multiple Choice Test, Form B DOK: DOK 2

3. ANS: B PTS: 1 DIF: Average TOP: Chapter 3 Multiple Choice Test, Form B DOK: DOK 1


5. ANS: A PTS: 1 DIF: Average TOP: Chapter 3 Multiple Choice Test, Form B DOK: DOK 2

6. ANS: J PTS: 1 DIF: Average TOP: Chapter 3 Multiple Choice Test, Form B DOK: DOK 2

7. ANS: C PTS: 1 DIF: Average NAT: NT.CCSS.MTH.10.9-12.G.SRT.5TOP: Chapter 4 Multiple Choice Test, Form B DOK: DOK 2


9. ANS: D PTS: 1 DIF: Average TOP: Chapter 5 Multiple Choice Test, Form B DOK: DOK 2

10. ANS: J PTS: 1 DIF: Average TOP: Chapter 5 Multiple Choice Test, Form B DOK: DOK 2

11. ANS: B PTS: 1 DIF: Average TOP: Chapter 5 Multiple Choice Test, Form B DOK: DOK 2

SHORT ANSWER

1. ANS: 112°

PTS: 1 DIF: Average TOP: Chapter 1 Multiple Choice Test, Form BDOK: DOK 2

2. ANS: ∠1 and ∠5


3. ANS: 32.8 cm


ID: A

2

4. ANS: −6, −2.5ÊËÁÁ

ˆ̃̃


5. ANS: 14, −8ÊËÁÁ

ˆ̃̃


6. ANS: 13 units


7. ANS: 2 units to the right and 3 units down


8. ANS: −16


9. ANS: If a number is not divisible by 6, then it is not divisible by 3.


10. ANS: Sym. Prop. of ≅


11. ANS: x


ID: A

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12. ANS: Conditional: If all four sides of the rectangle have equal lengths, then it is a square.Converse: If a rectangle is a square, then its four sides have equal lengths.Let p and q represent the following.p: A rectangle is a square.q: All four sides of the rectangle have equal lengths.

The two parts of the biconditional p ↔ q are p → q and q → p.

Conditional: If all four sides of the rectangle have equal lengths, then it is a square.Converse: If a rectangle is a square, then its four sides have equal lengths.

PTS: 1 DIF: Average REF: 19d5c172-4683-11df-9c7d-001185f0d2eaOBJ: 2-4.1 Identifying the Conditionals Within a Biconditional StatementTOP: 2-4 Biconditional Statements and Definitions KEY: biconditionalDOK: DOK 2

13. ANS: [1] Addition Property of Equality;[2] Division Property of Equality

4x − 6 = 34 Given equation+6 +6 [1] Addition Property of Equality

4x = 40 Simplify.4x4

= 404 [2] Division Property of Equality

x = 10 Simplify.

PTS: 1 DIF: Basic REF: 19dce886-4683-11df-9c7d-001185f0d2eaOBJ: 2-5.1 Solving an Equation in Algebra NAT: NT.CCSS.MTH.10.9-12.A.REI.1TOP: 2-5 Algebraic Proof KEY: algebraic proof | proofDOK: DOK 2

14. ANS: Transitive Property of CongruenceThe Transitive Property of Congruence states that if figure A ≅ figure B and figure B ≅ figure C, then figure A ≅ figure C.

PTS: 1 DIF: Basic REF: 19e1ad3e-4683-11df-9c7d-001185f0d2eaOBJ: 2-5.4 Identifying Properties of Equality and Congruence TOP: 2-5 Algebraic Proof KEY: congruence properties | reflexive | symmetric | transitiveDOK: DOK 1

ID: A

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15. ANS: [1] AB +BF = FC+CD[2] AB +BF = AF ;FC+CD = FDIn a flowchart, reasons flow from the statement above. The statement above Reason 2 is AB +BF = FC+CD. The statement above Reason 3 is AB +BF = AF ; FC+CD = FD.

PTS: 1 DIF: Average REF: 19eb0f9e-4683-11df-9c7d-001185f0d2eaOBJ: 2-7.1 Reading a Flowchart Proof TOP: 2-7 Flowchart and Paragraph ProofsKEY: flowchart proof | two-column proof DOK: DOK 2

16. ANS: perpendicular segments

PTS: 1 DIF: Average NAT: NT.CCSS.MTH.10.9-12.G.CO.1TOP: Chapter 3 Multiple Choice Test, Form B DOK: DOK 1

17. ANS: supplementary


18. ANS: EF


19. ANS: zero


20. ANS:

− 13


21. ANS: parallel


22. ANS: A rotation 180° with center of rotation 0, 0Ê

ËÁÁˆ̃̃.

PTS: 1 DIF: Average NAT: NT.CCSS.MTH.10.9-12.G.CO.6TOP: Chapter 4 Multiple Choice Test, Form B DOK: DOK 2

ID: A

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23. ANS: scalene acute


24. ANS: 8

PTS: 1 DIF: Average NAT: NT.CCSS.MTH.10.9-12.G.SRT.5TOP: Chapter 4 Multiple Choice Test, Form B DOK: DOK 2

25. ANS: 120


26. ANS: 4


27. ANS: SAS

PTS: 1 DIF: Average NAT: NT.CCSS.MTH.10.9-12.G.CO.10 | NT.CCSS.MTH.10.9-12.G.SRT.5TOP: Chapter 4 Multiple Choice Test, Form B DOK: DOK 2

28. ANS: HL


29. ANS: 12


30. ANS: CPCTC


31. ANS: 45


ID: A

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32. ANS: 3.05


33. ANS: 46


34. ANS: 6 2


35. ANS: 13


36. ANS: 5 2

2


ID: A

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37. ANS: y − 3 = − 7

2 (x − 1.5)

Step 1 Plot AB.

The perpendicular bisector of AB is perpendicular to AB at its midpoint.

Step 2 Find the midpoint of AB.

Midpoint of AB = −2 + 52

, 2 + 42

Ê

Ë

ÁÁÁÁÁÁ

ˆ

˜̃̃˜̃̃ = (1.5,3)

Step 3 Find the slope of the perpendicular bisector.

Slope of AB =(4) − (2)

(5) − (−2)= 2

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Since the slopes of perpendicular lines are opposite reciprocals, the slope of the perpendicular bisector is − 72 .

Step 4 Use point-slope form to write the equation.y − y 1 = m(x − x 1 )

y − 3 = − 72 (x − 1.5)

PTS: 1 DIF: Average REF: 1ad27b8a-4683-11df-9c7d-001185f0d2eaOBJ: 5-1.4 Writing Equations of Bisectors in the Coordinate Plane NAT: NT.CCSS.MTH.10.9-12.G.GPE.5 TOP: 5-1 Perpendicular and Angle BisectorsKEY: point-slope form | perpendicular bisector |coordinate geometry DOK: DOK 2

38. ANS: plane BAD


ID: A

8

39. ANS: 40


geometry midterm review - quia · geometry midterm review multiple choice identify the choice that...

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