Chapter 6 Practice TestMultiple Choice Identify the choice that best completes the statement or answers the question. ____ 1. Find the values of the variables and the lengths of the sides of this kite.

||

3x + 5

a. x =7, y = 2; 4, 4 b. x =7, y = 2; 1, 9 ____ 2. Which statement is true? a. All squares are rectangles. b. All parallelograms are rectangles. c. All rectangles are squares. d. All quadrilaterals are rectangles.

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x+ 9

____

3. Judging by appearances, which figure is a trapezoid? a. c.

b.

|

y3 |

x+ 2

c. x = 2, y = 7; 4, 11 d. x = 2, y = 7; 1, 9

d.

____

4. ABCD is a parallelogram. IfA B

then

The diagram is not to scale.

D

C

a. 120 ____

b. 140

c. 110 then

d. 70 The diagram is not to scale.

5. ABCD is a parallelogram. IfA B

D

C

a. 66 ____

b. 56

c. 149

d. 124

6. LMNO is a parallelogram. If NM = x + 12 and OL = 5x + 4 find the value of x and then find NM and OL.O N

L

M

a. x = 4, NM = 16, OL = 16 b. x = 2, NM = 14, OL = 14 ____ 7. For the parallelogram, if3 4

c. x = 4, NM = 14, OL = 16 d. x = 2, NM = 16, OL = 14 and find The diagram is not to scale.

2

1

a. 18

b. 138

c. 148

d. 42

____

8. Find the values of the variables in the parallelogram. The diagram is not to scale.23 105

y z x

a. b. ____

c. d.

9. WXYZ is a parallelogram. Name an angle congruent toX Y

N

W

Z

a. ____ 10. In the parallelogram,J

b. andK

c. Find

d. The diagram is not to scale.

O

M

L

a. 80

b. 97

c. 107

d. 27

____ 11. In parallelogram DEFG, DH = x + 4, HF = 3y, GH = 3x 1, and HE = 2y + 1. Find the values of x and y. The diagram is not to scale.D E

H G F

a. x = 2, y = 2

b. x = 2, y = 2

c. x = 3, y = 5

d. x = 5, y = 3 Find JM. The diagram is not to scale.

____ 12. In the figure, the horizontal lines are parallel andM L K J 7 B C D A

a. 7

b. 28

c. 21

d. 14 Find KL and FG. The diagram is not to

____ 13. In the figure, the horizontal lines are parallel and scale.M L K J 8.7 C D B A H G F 6.6 E

a. b. KL = 6.6, FG = 6.6

c. KL = 8.7, FG = 8.7 d. KL = 8.7, FG = 6.6

____ 14. Find AM in the parallelogram if PN =15 and AO = 5. The diagram is not to scale.M N

A

P

O

a. 5

b. 15

c. 7.5

d. 10

____ 15. What is the missing reason in the proof? Given: parallelogram ABCD with diagonal Prove:A B

D

C

Statements 1. 2. 3. 4. 5. 6. a. SSS b. ASA

Reasons 1. Definition of parallelogram 2. Alternate Interior Angles Theorem 3. Definition of parallelogram 4. Alternate Interior Angles Theorem 5. Reflexive Property of Congruence 6. ? c. Alternate Interior Angles Theorem d. Reflexive Property of Congruence

____ 16. Find values of x and y for which ABCD must be a parallelogram. The diagram is not to scale.A3x 2 y + 19 5y 5 x+ 2

B

D

C

a. x = 2, y = 4

b. x = 6, y = 2

c. x = 2, y = 25

d. x = 2, y = 6

____ 17. Based on the information in the diagram, can you prove that the figure is a parallelogram? Explain.

a. b. c. d.

Yes; two opposite sides are both parallel and congruent. Yes; the diagonals bisect each other. No; you cannot prove that the quadrilateral is a parallelogram. Yes; the diagonals are congruent.

____ 18. Based on the information given, can you determine that the quadrilateral must be a parallelogram? Explain. Given:X

andY

N

W

Z

a. b. c. d.

Yes; diagonals of a parallelogram bisect each other. Yes; two opposite sides are both parallel and congruent. No; you cannot determine that the quadrilateral is a parallelogram. Yes; opposite sides are congruent.

____ 19. If and be a parallelogram. The diagram is not to scale.O N

find the values of x and y for which LMNO must

L

M

4 11 x = 8, y = b. 11 x = 8, y = 4a. ____ 20. IfA

11 x = 13, y = 4 d. 4 11 x = 13, y =c. findB

so that quadrilateral ABCD is a parallelogram. The diagram is not to scale.

D

C

a. 70

b. 145

c. 35

d. 290

____ 21. Which statement can you use to conclude that quadrilateral XYZW is a parallelogram?X Y

N

W

Z

a. b.

c. d.

____ 22. In the rhombus, not to scale.

Find the value of each variable. The diagram is

|

3 2|

1|

a. x = 15, y = 75, z = 30 b. x = 30, y = 75, z = 60

|

c. x = 30, y = 165, z = 30 d. x = 15, y = 165, z = 60

____ 23. DEFG is a rectangle. DF = 5x 2 and EG = x + 38. Find the value of x and the length of each diagonal. a. x = 5, DF = 43, EG = 43 c. x = 10, DF = 48, EG = 51 b. x = 10, DF = 43, EG = 43 d. x = 10, DF = 48, EG = 48 ____ 24. Lucinda wants to build a square sandbox, but has no way of measuring angles. Explain how she can make sure that the sandbox is square by only measuring length. a. Arrange four equal-length sides so the diagonals bisect each other. b. Arrange four equal-length sides so the diagonals are equal lengths also. c. Make each diagonal the same length as four equal-length sides. d. Not possible; Lucinda has to be able to measure a right angle. ____ 25. Which description does NOT guarantee that a quadrilateral is a parallelogram? a. a quadrilateral with consecutive angles supplementary b. a quadrilateral with the diagonals bisecting each other c. a quadrilateral with both pairs of opposite sides congruent d. quadrilateral with two opposite sides parallel ____ 26. Find the values of a and b.The diagram is not to scale.a 116

49

b

a. b.

c. d.

____ 27. The isosceles trapezoid is part of an isosceles triangle with a 32 vertex angle. What is the measure of an acute base angle of the trapezoid? Of an obtuse base angle? The diagram is not to scale.

a. 32; 106 ____ 28. Find

b. 74; 106

c. 74; 148

d. 32; 148

in the kite. The diagram is not to scale.A 27 1 2| |

D

3

B

C

a. 63, 63

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____ 29. Which description does NOT guarantee that a trapezoid is isosceles? a. congruent diagonals b. congruent legs c. both pairs of base angles congruent d. congruent bases ____ 30. a. 157 ____ 31. andR| |

are base angles of isosceles trapezoid JKLM. If b. 1 Find c. 23 The diagram is not to scale.

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b. 27, 63

c. 27, 27

d. 63, 27

and d. 78.5

U

S

||

T

a. 90

||

b. 45

c. 65

d. 70

____ 32. One side of a kite is 4 cm less than four times the length of another side. The perimeter of the kite is 68 cm. Find the lengths of the sides of the kite. a. 19 cm and 72 cm c. 7.6 cm and 26.4 cm b. 7.6 cm d. 19 cm

Essay 33. Given: Prove: VX = XT

V

U

X

S

T

Chapter 6 Practice Test

Answer SectionMULTIPLE CHOICE 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS: C A D C D B B A D C B C D A B D B D C B C A D B D C B B D A A

32. ANS: C ESSAY 33. ANS: