Math 3 Unit 6: Geometry Name:Date Homework

1

Solving systems of linear equations by graphing (on graph paper):1. Graph each equation on the same coordinate plane2. The solution is the point(s) where the lines intersect

A system of linear equations will have: Solution0 solutions if the lines are parallel No Solution or { } or ⌀1 solution if the lines intersect in a single point

(x , y)[The point of intersection is the solution.]

Infinitely many solutions if the lines are the same line

Infinitely many solutions on y = mx + b[All points on the given lines are solutions.]

I. Graph the following. State the solutions as an ordered pair, no solution Ø, or infinitely many solutions on [ the equation of the line ]. For #6,7 use the same grid

1. 2. 3.

4. 5. 6x – 2y = 2 6. y = x + 2 7. y =

–3x – 4

2x + y = 4 x – y = 4 3x +

y = –4

2

II. To solve using a graphing calculator: 1. Write each equation in slope intercept form. 2. Put in 3. Use the graphing calculator to find the solution of each system (round to nearest hundredth if necessary).

8. 9. 10.

11. 12. 12.

2 METHODS to Solve systems algebraically: 1. Substitution 2. EliminationSteps By Substitution:1. Get one of the equations in terms of one of the variables.2. Substitute new equation into the other original equation.3. Solve for the remaining variable. (There should only be one now!)4. Substitute that answer into one of the original equations and solve.5. Write answer as a point (ordered pair).

Steps By Elimination:1. Pick a variable to eliminate (get rid of).2. Multiply both equations by a number so the like variables have opposite coefficients.3. Add (combine) the equations together and solve.4. Plug the answer into one of the original equations and solve.5. Write answer as a point (ordered pair).

REMEMBER: If both the variables cancel out, TRUE EQUATION: infinitely many solutions on the line. FALSE EQUATION: no solution.

Ex 1. By ___________________________ Ex 2. By _________________________3a – 2b = – 3 3c +9d = 2

3a + b = 3 c + 3d =

Solve using Substitution or Elimination.

1. 2x + 4y = 8 2. x + 2y =11 3. 5x + 3y = 9 3x + 6y = 18 x – 2y = -1 2x – 4y = 14

4. 2x – y = 1 5. 2x – 3y = -7 6. x – 2y = 3 4x – 2y = 2 3x + y = -5 2x + 4y = 1

3

Y= 2nd Trace #5intersect

Enter 3 times

Day 1 HW. Directions: For problems 1-6, solve by substitution. For problems 7-12, solve by elimination.

__________1. 4x 3y 1 __________2 . 2x y 6 x 1 y x y 1

___________3. 6x y 5 ___________4 . 2x 3y 7 4x 2y 2 x 1 4y

___________5 . 2x 3y 6 ____________6 . 6x 2y 8 x 3y 15 y 3x 4

____________7 . 2y 5x 1 _____________8 . 4x 3y 1x 2y 5 3x 5y 13

_____________9 . 3x y 2 ______________10. 3x 6y 427x 8y 1 x 2y 14

_____________11. 9y 2x 7 _______________12. 3x 5y 8x 3y 5 4x 7y 12

Angle Relationships4

49°

Definition Example Non-exampleADJACENT

ANGLES

VERTICAL ANGLES

LINEAR PAIR

PERPENDICULARLINES

COMPLEMENTARYANGLES

SUPPLEMENTARY ANGLES

ANGLE BISECTOR

Identify each pair of angles as adjacent, vertical, and/or linear pair.1. 1 and 2 2. 1 and 6 3. 1 and 5

4. 3 and 2 5. 5 and 2 6. 3 and 6

Find the measure of the angle.7. BCD 8. BCE 9. DCE

10. ECF 11. ACB 12. ACD

Use the figure at the right.13. Name two acute vertical angles. 14. Name two obtuse vertical angles.

15. Name a linear pair. 16. Name two acute adjacent angles.

17. Name an angle supplementary to FKG.

18. Find the measure of an angle supplementary to 50°. 19. Find the measure of an angle complementary to 50°

20. Find the measure of an angle supplementary to 107°. 21. Find the measure of an angle complementary to 107°.Day 2 notes Geometry Review: Angles

5

Two angles are ________________ if their sides form two pairs of opposite rays.

Examples: vertical angles are always ______________

Two angles are ________________ if they have a common side, a common vertex, and no common interior points.

Examples:

Two angles are _______________________________ if the sum of their measures is 90. Each angle is a complement of the other.

Examples:

Two angles are ________________________________ if the sum of their measures is 180. Each angle is a supplement of the other.

Examples:

Linear Pair: Two ____________ angles whose non-common sides form a _______________.

A linear pair is always ____________________________

m∠1 + m∠2 = _________°

Label the diagram to the right so that m∠BGC=33 and m∠DGE=57

1. ∠FGA ≅ _________ 2. m∠CGD = ______° 3. m∠AGB = ______°

4. m∠AGE = ______° 5. m∠AGC = _____° 6. m∠BGD= ______°

7. ∠BGF and _________ are supplementary

8. ∠EGC and ________ are supplementary

9a. Are ∠AGF and ∠CGD supplementary?__________why/why not?

9b. Are they a linear pair?__________why/why not?Solve the following for the indicated variable. Set up an equation using the angle relationships

6

x + 16 2x – 16

3x – 5 6x – 23

1 2

12

34

35

55

A

BC

E D

1 2 3

________________ 1. ___________________ 2.

_________________ 3. ____________________ 4.

Fill in the blank with an appropriate word.

_________________________ 1. The supplement of a right angle is a ___angle.

_________________________ 2. The supplement of an obtuse angle is a(n)___angle.

__________________________ 3. The supplement of an acute angle is a(n) ____angle.

__________________________ 4. Vertical angles are _____.

___________________________ 5. _____lines form right angles.

__________________________ 6. Congruent supplementary angles each have a measure of ______.

__________________________ 7. Congruent complementary angles each have a measure of _____.

8. The angles in a linear pair are ________________________ and ____________________________.

9. m∠1 = 40. What is the measure of its complement? __________ Its supplement? ____________

10. m∠2 = 120. What is the measure of its complement? __________ Its supplement?____________

11. m∠A = x. What is the measure of its complement? _____________ Its supplement? _____________

12. The measure of a supplement of an angle is 15 more than 2 times the complement. Find the measures of the angle, the complement, and the supplement.

Triangle Sum Theorem –

7

3x – y 50

x

2x – 36

3x – 8 x

2y – 17

Exterior angle of a triangle:

Name the exterior angles shown of the triangle:

Remote Interior’s:

Name the remote interior ’s for 2:__________ for 7: __________for 4:__________

Measure of an Exterior = Sum of the measures of its Remote Interior ’s.

m7 = ______+ _______ m2 = ______+ _______ m4 = _______+ ________

Is 3 an exterior angle? ____________ Why/why not? ____________________________________________________

Examples: Find the value of the variable(s) in each figure below.

1. 2. 3. 4.

5. 6. 7. 8.

9. 10. 11.

12.

Day 2 HW

8

1 234

5

67

A

CBD

19x - 15

26x + 20 9x + 25

I. Solve using algebra. Define the variable and write an equation for full credit.1.. Four times the complement of an angle is 45 less than its supplement. Find the measures of all 3 ’s.

2. A B. Find x and the mA.

3. Find the measure of each angle, if m 1 = x, m 2 = 3x , m 3 = 2x.

4. Find the value of x, mABC, and mABD. 5. Find x and y so that

6. BC bisects ABD. If mABC = 4x and mCBD = x + 60, find mABD.

7. Find mQRT if mQRT = 3x + 8 and mTRS = 2x + 7.

8. Find the measure of an angle and its complement if one angle measures 6 more than twice the other.

9. Find the measure of an angle and its supplement if one angle measures 7 less than the other.

II. Given: ∠1 is a right angle, m∠5=30, and ∠2 ≅ ∠3. Find the following

1. m∠1=______ m∠2=_____ m∠3=_____ m∠4=_____ m∠6=_____ m∠7=_____

2. Name all vertical angles___________________________________________

3. Name two complementary angles_________________ 4. m∠3 + m∠2 +m∠1 = ___________

9

172

35

2x + 5A 4x B

1 2 3

Q R S

TC

B

AD

A

CB

D

E

3x° (2x+50)°

●6

4

10. 11.

Day 3 notes Parallel Lines

Define Transversal:

10

III

When 2 coplanar lines are cut by a transversal, 8 angles are formed:

INTERIOR ’s: EXTERIOR ’s: LINEAR PAIRS: VERTICAL ’s:

TYPES OF ANGLES

Alternate Interior ’s:

Name the Alt. Int. ’s:

Same–Side Interior ’s (consecutive int. ’s):

Name the S.S.int. ’s:

Corresponding ’s:

Name the Corr. ’s:

Alternate Exterior ’s:

Name the Alt. Ext. ’s:

11

1 23 4

5 67 8

1 23 4

567 8

a

b

c

46

31 2

75

8

46

31 2

75

8

46

31 2

75

8

46

31 2

75

8

Use the given line as a transversal:

1. Name alt. int ’s using line x:

2. Name s.s. int. ’s using line y:

3. Name corr. ’s using line z:

4. Name alt. ext. ’s using line y:

5. Name alt. int. ’s using line z:

6. Name s.s. int ’s using line z:

Corresponding Angles Postulate: If two parallel lines are cut by a transversal, then the pairs of corresponding angles are congruent. You may write: If 2 ║ lines are cut by a transversal, then corr. s R .

Alternate Interior Angles Theorem: If two parallel lines are cut by a transversal, then the pairs of alternate interior angles are congruent.

You may write:

2 ║ lines are cut by a transversal, then alt.int. s R .

Alternate Exterior Angles Theorem: If two parallel lines are cut by a transversal, then the pairs of alternate exterior angles are congruent.

You may write: If 2 ║ lines are cut by a transversal, then alt. ext. s R .

Same-Side Interior Angles Theorem: If two parallel lines are cut by a transversal, then same-side interior angles are supplementary.

You may write: If 2 ║ lines are cut by a transversal, then s.s.int. s R sup..

Properties of Parallel LinesSolve for x, y and z.1. 2. 3.

12

xy

z

12

34

5678

91011

12

6y

3y

5x

5y 8x

4x

140

(2x + 10)

y

4 5. 6.

7. 8.

9. 10.

Day 3 HW1. a) Find the measure of each angle in the diagram.

13

3z + 8 4y + 14

70 x

x

5y2z

40

x 40 y

70

65 x

55

y

50

40

x

y

5z

3x

60 2y + 10

30y x

426z

e

b

c

d

af g

hij

k55°

110°

Angle Measure

a

b

c

d

e

f

g

h

i

j

k

b) What geometric relationship did you use to find angles c, g, and k?

Explanation for c:

Explanation for g:

Explanation for k:

2. Use the diagram to answer the questions below.

a. If angle 1 and angle 7 are congruent, what property proves the lines are parallel?

b. If angle 5 and angle 8 are congruent, what can be concluded about the lines?

c. If the lines are parallel, what must be true about angle 2 and angle 6? What is the name of the property used to determine this?

d. If the lines are parallel, what must be true about angle 7 and angle 3? What is the name of the property used to determine this?

3. Set up and solve an equation to solve for x in each diagram.

a) b) c) d)

14

1 23 45 78

6

3x – 20 2x + 20 3x – 20 2x + 203x + 2

7x – 10

98

x48

Day 3 HW

Assume a ⁄⁄ b. Complete the chart.ANGLES TYPE , SUPPL., OR NONE1. 1 and 14

2. 2 and 15

3. 7 and 9

4. 9 and 16

5. 10 and 17

6. 16 and 14

7. 9 and 14

8. 18 and 19

9. 1 and 16

10. 3 and 8

11. 6 and 9

12. 12 and 13

13. 7 and 11

14. 6 and 8

15. 4 and 13

16. 9 and 12

15

2

5

16

7

8

34

9

1012

111314

1516

17

1819

bx

ya

Extra Practice: Identify each as alternate interior, alternate exterior, corresponding, or same side interior.

___________________________ __________________________ _______________________

____________________________ __________________________ _______________________

____________________________ _________________________________________________

10) Find the measure of each angle:11) 11) 12)

___________________________________13)

14)15)

Solve for x. 16) 17) 18)

16

x

More Triangle Practice. Solve for x.1. 2. 3.

4. 5. 6.

7. 8. 9.

10. 11. 12.

17

140x

x 41

x

41

39

2727

x

x

28

45

62

36°

60°

Special Segments of a :

Def: A median of a triangle is _______________________________________________________________________

Draw the three medians of the following triangle:

The point of concurrency of the three medians of a triangle is called the _______________.

The distance from the centroid to a midpoint is x .The distance from the centroid to a vertex is 2x .The distance from the midpoint to a vertex would be 3x.

Examples: Given W is the centroid of QRS:

1. Ratio of WB to QW: _________2. Ratio of WB to QB: _________3. Ratio of QW to QB: __________4. QB = 12; QW = ______5. RW = 6; RA = ______6. CW = 5; SW = _____

7. RW = 2x + 8, WA = 4x – 5 find x.

8. SW = 4x + 1, SC = 9x + 6, find x.

9. In ABC, G is the centroid and BE = 9. Find BG and GE.

Def: An altitude of a triangle is ____________________________________________________

________________________________________________________________________.Draw the altitude from all three vertices:

18A J

Q

C

R

A

SB

W

10. Name a median for ABC:

The point of concurrency of the lines containing the altitudes of a triangle is called the __________________.

Def: An Angle bisector is ____________________________________________________

Draw the angle bisectors of all 3 vertices:

The point of concurrency of the bisectors of the angles of a triangle is called the ___________________.

Perpendicular bisector of a segment:__________________________________________.

Draw the perpendicular bisectors of each side of the :

The point of concurrency of the bisectors of the sides of a triangle is called the

__________________.THEOREMS:

If a point lies on the perpendicular bisector of a segment, then the point is equidistant from the endpoints of the segment.

If a point is equidistant from the sides of an angle of a triangle, then the point lies on the bisector of the angle.

19

B DO Y

N U

R

C

T

E

A B

l

P

A

B C

ED

F

#1. Q is equidistant from the sides of Find the value of x. The diagram is not to scale.

#3. What is the name of the segment inside the large triangle?

#4. For a triangle, list the respective names of the points of concurrency of:a) Perpendicular bisectors of the sides b) bisectors of the angles c) medians d) lines containing the altitudes

________________________ _________________________ _______________________ ________________________

Definition:The mid-segment of a triangle is a segment joining the

__________________of two sides of a triangle

Properties of a mid-segment:

1. is ____________ to the third side20

#2. Name the point of concurrency of the angle bisectors.

#5. In ABC centroid D is on median . and Find AM.

2. is ____________ as long as the third side.

M, N , and P are midpoints of and , respectively.

1.) Mark the diagram with tick marks:2) Name all ’s:

3) // _____; // _____; // ____

4.) Given DE, DF, and FE are the lengths of mid-segments. Find the perimeter of triangle ABC.

5. Given AC = 42, CB = 46, AB = 48.D, E, F are midpoints. Find the perimeter of triangle DEF.

6.) D, E are midpoints.  Find the measure of <A.

8.) Given:  A(-3,2),  B(2,3), C(1,-1) as the midpoints of the sides of triangle DEF. 21

Z

M N

X YP

7. Find the value of x. The diagram is not to scale.

Find the coordinates of the vertices of triangle DEF. INCLUDEPICTURE "https://www.lakesideschool.org/../../Program Files/TI Education/TI InterActive!/TIIimagefile5968.gif" \* MERGEFORMATINET INCLUDEPICTURE "https://www.lakesideschool.org/../../Program Files/TI Education/TI InterActive!/TIIimagefile5968.gif" \* MERGEFORMATINET INCLUDEPICTURE "https://www.lakesideschool.org/../../Program Files/TI Education/TI InterActive!/TIIimagefile5968.gif" \* MERGEFORMATINET INCLUDEPICTURE "https://www.lakesideschool.org/../../Program Files/TI Education/TI InterActive!/TIIimagefile5968.gif" \* MERGEFORMATINET INCLUDEPICTURE "https://www.lakesideschool.org/../../Program Files/TI Education/TI InterActive!/TIIimagefile5968.gif" \* MERGEFORMATINET INCLUDEPICTURE "https://www.lakesideschool.org/../../Program Files/TI Education/TI InterActive!/TIIimagefile5968.gif" \*

MERGEFORMATINET

10. Find the value of x. 11. Identify the mid-segment and find its length.

12. Given : Find ED if BC = x2 – 7x and ED = x + 5

22

9. Points B, D, and F are midpoints of the sides of EC = 30 and DF = 23. Find

AC.

C

B

A

Y X

Z

6

6

5 5

7

6

B

A

C

E D

Day Homework1. Identify as a median, a mid-segment, an altitude, a perpendicular bisector, an angle bisector or

none of these in each of the following pictures:

a. b. c.

d. e. f.

2. Use the picture to the right to answer the following questions:

a. If BD = 8x + 7 and DA = 4x + 35, then:

x = __________ BD = __________ DA = __________

b. If BC = 26, then DE = __________

c. If AE = 32, then DF = __________

d. If FE = 3x + 8 and AB = 8x – 14, then:

x = __________ FE = __________ AB = __________

e. If DE = 4x + 6 and BC = 6x + 32, then:

x = __________ DE = __________ BC = __________

3. Use the picture to the right to answer the following questions:

a. If CD = 36, then CG = __________ and GD = __________

b. If FG = 14, then GA = __________ and FA = __________

c. If BG = 22, then GE = __________ and BE = __________

d. IF BF = 3x + 12 and FC = 5x – 26, then:

x = __________ BF = __________ FC = __________

e. If BD = 7x + 4 and DA = 5x + 28, then:

23

x = __________ BD = __________ DA = __________4. Use the picture to the right and the fact that is the perpendicular bisector of to answer the

following questions: Mark the diagram.

a. If AD = 56, then AB = __________

b. mCDA = __________ and mCDB = __________

5. Use the picture to the right and the fact that F is on the bisector of DAE to answer the following questions:

a. If mDAF = 43, then mEAG = __________

b. If DG = 22, then GE = __________

6. What is the key information to know about a median?

7. What is the key information to know about a perpendicular bisector?

8. What is the key information to know about a mid-segment?

9. What is the key information to know about an altitude?

10. What is the key information to know about an angle bisector?

Peanut Butter Chocolate And Bananas In My Cereal Are Okay

24

Day 7 Parallelograms

I. 1-8, Given Parallelogram PQRS, state the property that justifies each statement. A. Opposite sides are parallel (definition)B. Opposite sides are congruentC. Opposite ∠’s are congruentD. Consecutive ∠’s are supplementaryE. Diagonals bisect each other

Write the letter only.______1. _______5. m∠SPQ + m∠PQR = 180

______2. _______6.

______3. _______7.

______4.∠PSR ≅ ∠PQR _______8. ∠PSR and ∠SRQ are supplementary

FIND ANGLE MEASURE AND LENGTHS:II. ACEF and BCDG are parallelograms.

______9. m∠C ______13. FE

______10. m∠G ______14. AF

______11. m∠GDC ______15. BG

______12. m∠GBC ______16. DG

III. MECO and EXIC are coplanar parallelograms and ∠x is a right ∠.

_______17. OC ______20. m∠I

_______18. CI ______21. m∠M

_______19. XI ______22. m∠XEM

IV. Given the parallelogram SALT with LO = 9cm and AO = 16cm.

________23. SO________24. OT________25. SL

25

P Q

RS

O

CBA

EF

G D

8 6

70

4

3

T L

AS

O

M

E X

IC

O

108

1204

Parallelograms

Definition:

Theorem 6-1:

Ex 1: Solve for x and y. Ex 2: Solve for x and y. Ex 3: Solve for x and find AB.

Theorem 6-2:

Ex 4: Solve for x and y. Ex 5: Solve for x and y& find and .

26

˚

˚

˚ ˚

A parallelogram is a quadrilateral with two pairs of opposite sides parallel.

If a quadrilateral is a parallelogram, then both pairs of opposite sides are congruent.

If a quadrilateral is a parallelogram, then both pairs of opposite angles are congruent.

Theorem 6-3:

Ex 6: If , find , and . Ex 7: Find and .

Theorem 6-4:

For examples 8 – 11, use the figure to the right.

Ex 8: If AE = 8, find EC.

Ex 9: If EB = 12 and DE = 3x, solve for x.

Ex 10: If DE = 7x + 2 and EB = 9x – 6, find DB.

Ex 11: If EC = 3x – 8 and AC = 4x +6, solve for x and find AC.

In examples 12 – 13, ABCD is a parallelogram.

Ex 12: Solve for x. Ex 13: Solve for x and y.

27

˚

If a quadrilateral is a parallelogram, then consecutive angles are supplementary.

If a quadrilateral is a parallelogram, then the diagonals bisect each other.

˚ ˚

˚

Ex 14: Given that ABCD is a parallelogram, if and , find

(a)

(b)

Ex 15: Given that ABCD is a parallelogram, find the following:

(a) = (b) =

(c) = (d) =

(e) = (f) =

(g) DE =

Special ParallelogramsRECTANGLE

Definition: Theorem 6-9:

Use rectangle ABCD to answer the following:

1. If EB = 12, then AE =

2. If EC = 12x – 4 and DE = 44, then x =

3. If AE = 5x – 2 and DB = 6x + 16, then AC =

4. If , then = 5. If , then = and =

6. If and , then x =

7. If and , then = _________ and = __________

8. If and , then = 9. If and , then =

28

˚

˚

˚

A rectangle is a parallelogram with 4 right angles.

If a parallelogram is a rectangle, then its diagonals are congruent.

RHOMBUS

Definition:

Theorem 6-11: Theorem 6-13:

Use rhombus ABCD to answer the following questions:

1. If AB = 7x + 3 and DC = 10x – 6, then AD =

2. If AC = 32, then EC =

3. If and , then x =

4. If and , then =

5. If , then = and =

6. If , then =

SQUARE

Definition:

Use square ABCD to answer the following questions:

1. If AB = 2x + 3 and BC = 3x – 5, then DC =

2. Find and

3. If DB = 5x – 2 and EB = 2x + 4, then DB = and AE =

DAY 7 HWFor problems 1 – 6, ABCD is a parallelogram. Find the unknown measure.

1) If mDAB = 80˚, then mABC = __________

29

A rhombus is a parallelogram with 4 congruent sides.

If a parallelogram is a rhombus, then the diagonals are perpendicular.

If a parallelogram is a rhombus, then the diagonals bisect the angles they intersect.

A square is a parallelogram, a rectangle, and a rhombus.

A

B

C

D

E

2) If mADC = 127˚, then mCBA = __________

3) If DE = 6, then EB = _________ & DB = __________

4) If DC 14, then AB = _________

5) If AD = 3x + 6 and BC = x + 18, then x = _________ & AD = __________

6) If mCDB = 30˚ and mDBC = 40˚, then mDBA = _________ and mDAB = _________.

In each parallelogram below, find the values of the missing sides or angles.

7) AB = _________ 8) mA = __________

AD = _________ mBCD = _________

mA = _________ mCDE = _________

mD = _________

9) mDCA = ________ 10) mECD = ________

mCAD = ________ mAED = ________

mCBA = ________ mABD = ________

BD = ___________

11) Given Rectangle BSTN find all interior angles.

Use square ABCD and the given information to find each value.

12. If mAEB = 3x, find x.

13. If mBAC = 9x, find x.

14. If AB = 2x + 4 and CD = 3x – 5, find BC

15. If mDAC = y and mBAC = 3x, find x and y.

Review 1Name the transversal and identify the special relationship. In the figure, lines m and p are parallel and m2 = 92° and

m12 = 74°. Find the measure of each angle.

11) m10 = ______30

A B

D C

10

8

62˚

A

B C

D E

44˚

D C

BA

83˚56˚

C

B A

D

E110˚

70˚

9

A

D

B

C

E

m

p

16

15

1413

1211

109

87

65

443

21

12) m8 = ______

13) m9 = ______

14) m5 = ______

15) m11 = ______

16) m13 = ______

Find the value of each variable in each figure.

17) 18) 19)

20) 21) 22)

Find the angle measures:

1.)

31

1) 14 and 15

2) 2 and 9

3) 8 and 4

4) 8 and 6

5) 5 and 10

6) 8 and 15

7) 13 and 11

8) 12 and 4

9) 8 and 11

10) 7 and 15

q

t

m18 17

16151413

1211

109

8 7 6 5

4321

p

m1 = ______ m8 = _____

m2 = ______ m9 = _____

m3 = ______ m10 = _____

m4 = ______ m11 = ______

m5 = ______ m6 = ______

m7 = ______

60

1 4032 4 5

6

78

9

10

20

11

25

2.)

3.) Given: a // b, find m1 = _________

Review 2 Section I1. Choose the best name for the parallelogram and 2. DEFG is a rectangle. Find the value of x and the length of each find the measures of the numbered angles. diagonal if DF = 2x – 1 and EG = x + 3.

32

m1 = ______ m8 = _____m2 = ______ m9 = _____m3 = ______ m10 = _____m4 = ______ m11 = ______m5 = ______ m12 = ______m6 = ______ m13 = ______m7 = ______

301

1312 50

11

9 8 7

2

10 34

30

72 6 5

What value of x and y will make the polygon a parallelogram?3. 4. 5.

Quadrilateral ABCD is a rhombus. 6.

7.

8.

9.

10.

HIJK is a rectangle. For the value of x and the length of each diagonal.

11. HJ = 3x + 7 and IK = 6x – 1112. HJ = 19 + 2x and IK = 3x + 22

ABCD is a rectangle. The diagonals intersect at E. Find x and y.13.

14.

Given rhombus ABCD whose diagonals intersect at E.

15. AB = 7x2 + 28 , DC = x2 + 31x. Find AC.16.

Find the length or angle measure.

17. WXYZ is a square. WX = 1 – 10x, YZ = 14 + 3x, find XY.18. WXYZ is a rhombus. 19. WXYZ is a rectangle. The perimeter of ∆XYZ = 24. XY + YZ = 5x – 1. XZ = 13 – x. Find WY.Check each box if the given statement is true for each quadrilateral.

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x + 2

6

y - 1

3x

(x+3y)°2x°

(3x+5)° 70°

x-56x

y 72

DC

A B

E

K

H I

J

D

A B

C

DC

A B

E

11. Points B, D, and F are midpoints of the sides of ACE. EC = 30 and DF = 23. Find AC.

12. Q is equidistant from the sides of TSR. Find mRST.

13. Where do the perpendicular bisectors of the sides of a right triangle intersect? ____________________________

14. Where do the bisectors of the angles of an obtuse triangle intersect? _____________________

15. Name a median shown for ABC. Name an angle bisector shown in ABC. Name an altitude shown in ABC.

16. In ABC, centroid D is on median . 17. B is the midpoint of .

AD = x + 4 and DM = 2x – 4 . Find AM. If BD = 5x + 3 and AE = 4x + 18, solve for x. Draw a diagram

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Parallelogram Rhombus Rectangle Square1. The diagonals are perpendicular.

2. The figure has four right angles.

3. The opposite sides are congruent.

4. The diagonals are congruent.

5. The figure has four congruent sides.

6. The diagonals bisect each other.

7. The consecutive angles are supplementary.

8. Each diagonal bisects a pair of opposite angles.

9. The figure has exactly four lines of symmetry.

10. The figure is a rectangle.

A

C F

D

B

E

B

A E

D

M

(2x + 5 )°

T

Q

(5x – 25 )°S

R