Free Printable Geometry: Topic 6 (Quadrilaterals & Other Polygons)

1.

Find the measure of DG.

a)

14

b)

28

c)

12

d)

16

2.

FEDC is an isosceles trapezoid. Find the missing angle.

a)

$180\degree$

b)

$140\degree$

c)

$120\degree$

d)

$60\degree$

3.

What is the SUM of the angle measures in a nonagon (9 sides)?

a)

1440°

b)

900°

c)

1080°

d)

1260°

4.

What is the sum of the exterior angles?

a)

180 degrees

b)

45 degrees

c)

360 degrees

d)

270 degrees

5.

Given a regular polygon. Determine is the value of x ?

a)

x =72 degrees

b)

x = 45 degrees

c)

x = 360 degrees

d)

x = 540 degrees

6.

Find the measure of one interior angle in each regular polygon. Round your answer to the

nearest tenth if necessary.

a)

A

b)

B

c)

C

d)

D

7.

If JL = 18, NK = 12, and ML = 10, find the perimeter of JKLM.

a)

A. 42

b)

B. 45

c)

C. 50

d)

D. 56

8.

If ABCD is a parallelogram, find m∠D.

a)

127

b)

112

c)

132

d)

146

9.

Find m∠P.

a)

107

b)

123

c)

142

d)

128

10.

Find the measure of angle T.

a)

116

b)

121

c)

126

d)

111

11.

If BD = 8x - 27 and EC = 2x + 33, find the length of BD.

a)

53

b)

61

c)

63

d)

56

12.

Find WX.

a)

29

b)

31

c)

22

d)

26

13.

If QRST is a kite, find the measure of angle QRS.

a)

137

b)

141

c)

124

d)

122

14.

Find the angle SUM of the interior angles of the polygon.

a)

720°

b)

900°

c)

1080°

d)

1260°

15.

Find the measure of ∠1:

a)

79°

b)

101°

c)

72°

d)

180°

16.

Given trapezoid ABCD, Find the value of x.

a)

7

b)

8

c)

85

d)

None of these

17.

Find the measure of n:

a)

117

b)

63

c)

25

d)

39

18.

Find the value of x.

a)

4

b)

6

c)

5

d)

129

19.

Find the measure of the midsegment XY:

a)

21

b)

9

c)

12

d)

10.5

20.

In parallelogram ABCD, $\angle DAB\ \cong\ ?$

a)

$\angle DAC$

b)

$\angle DCB$

c)

$\angle ABC$

d)

$\angle ADC$

21.

Find the measure of the angle indicated in the following parallelogram.

a)

95

b)

90

c)

81

d)

86

22.

Find the measure of the angle indicated in the following parallelogram.

a)

105

b)

36

c)

45

d)

135

23.

Find values of x and y for which ABCD must be a parallelogram. The diagram is not to

scale.

a)

x = 10, y = 13

b)

x = 5, y = 10

c)

x = 10, y = 21

d)

x = 10, y = 5

24.

If ACFG is a parallelogram with $m\angle CAG=\left(8a+13\right)\degree$ and $m\angle ACF\left(4a+23\right)\degree$ , find $m\angle ACF$ .

a)

$109\degree$

b)

$12\degree$

c)

$33\degree$

d)

$71\degree$

25.

In the parallelogram, $AX=4y+3$ and $XF=2y+7$ , find the value of y.

a)

5

b)

2

c)

2/3

d)

11

26.

The measure of the bases of a trapezoid are 14 and 20. What is the measure of the median (midsegment) of the trapezoid?

(a)

27.

WXYZ is an isosceles trapezoid with WX parallel to ZY. If $m\angle WZY=\left(2a-24\right)\degree$

and $m\angle XYZ=\left(a+37\right)\degree$ , find $m\angle XYZ$ .

a)

$98\degree$

b)

$55.7\degree$

c)

$102.7\degree$

d)

$61\degree$

28.

Two consecutive angles of a parallelogram measures (x + 30) and 2(x-30) respectively. What is the value of x?

a)

40

b)

50

c)

60

d)

70

29.

Two consecutive angles of a parallelogram measures (x+30) and 2(x-30) respectively. What is the measure of the smaller angle?

a)

20

b)

40

c)

60

d)

80

30.

What shape is this?

a)

Rectangle

b)

Kite

c)

Trapezoid

d)

Parallelogram

31.

(a)

32.

(a)

33.

(a)

34.

a)

A

b)

B

c)

C

d)

D

35.

Find the missing angle of the trapezoid.

a)

65

b)

115

c)

180

d)

None of these

36.

a)

A

b)

B

c)

C

d)

D

37.

Use the properties of isosceles trapezoids to solve for angle R.

a)

130 degrees

b)

50 degrees

c)

25 degrees

d)

Can't tell

38.

Find the value of x.

a)

4

b)

6

c)

5

d)

129

39.

What is the value of x?

a)

4

b)

360

c)

12

d)

6

40.

If you wanted to prove that Quadrilateral ABCD is a rhombus, what would be the best piece of evidence to use?

a)

The length of each side is √(34), therefore all sides are congruent.

b)

The length of each side 8, therefore all sides are congruent.

c)

The slope of AC and BD is 5/3, therefore AC and BD are parallel.

d)

The slopes of the sides are opposite reciprocals, therefore opposite sides are parallel.

41.

If you want to prove that Quadrilateral ABCD is a rectangle, what is the best piece of evidence to use?

a)

The lengths of AC and BD are the same, therefore AC and BD are congruent

b)

The slopes of AC and BD are the same, therefore AC and BD are congruent

c)

The slopes of AB and BD are the same, therefore AC is perpendicular to BD

d)

The slopes of AB and BD are opposite reciprocals, therefore AC is perpendicular to BD.

42.

What is the length of Side AC?

a)

5/2

b)

5

c)

29

d)

√(29)

43.

Fill in the missing reason for the proof.

a)

If alternate interior angles are congruent, then the lines are parallel.

b)

Definition of parallelogram

c)

Definition of parallel lines

d)

Opposite sides of a parallelogram are congruent.

44.

Fill in the missing reason for the proof.

a)

If alternate interior angles are congruent, then the lines are parallel.

b)

Definition of parallelogram

c)

Definition of parallel lines

d)

Opposite sides of a parallelogram are congruent.

45.

Which theorem can be used to prove the quadrilateral is a parallelogram?

a)

Parallelogram Opposite Sides Converse Theorem

b)

Parallelogram Opposite Angles Converse Theorem

c)

Opposite Sides Parallel and Congruent Theorem

d)

Parallelogram Diagonals Converse Theorem

46.

The missing reason is the same for steps 2 and 4. What is the missing reason?

a)

If alternate interior angles are congruent, then the lines are parallel.

b)

If vertical angles are congruent, then the lines are parallel.

c)

Definition of parallelogram

d)

Alternate interior angles formed by parallel lines are congruent.

47.

Choose the correct missing reasons for the proof.

a)

4) CPCTC; 6)All quads are parallelograms

b)

4) Alternate Interior Angles are congruent; 6) Definition of paralelogram

c)

4)CPCTC; 6)Definition of parallelogram

d)

4) Alternate Interior Angles are congruent; 6) All quads are parallelograms

48.

Which theorem can be used to prove the quadrilateral is a parallelogram?

a)

Parallelogram Opposite Sides Converse Theorem

b)

Parallelogram Opposite Angles Converse Theorem

c)

Opposite Sides Parallel and Congruent Theorem

d)

Parallelogram Diagonals Converse Theorem

49.

Which theorem can be used to prove the quadrilateral is a parallelogram?

a)

Parallelogram Opposite Sides Converse Theorem

b)

Parallelogram Opposite Angles Converse Theorem

c)

Opposite Sides Parallel and Congruent Theorem

d)

Parallelogram Diagonals Converse Theorem

50.

Why is this not a rhombus?

a)

Opposite sides are not congruent

b)

Angles are not all 90

c)

Diagonals don't meet at 90

d)

Same side angles don't add to 180

51.

Which method will NOT prove the quadrilateral is a parallelogram.

a)

Show that a pair of sides are congruent and parallel.

b)

Show that both pairs of opposite sides are congruent

c)

Show that both pairs of opposite sides are parallel

d)

Show that a pair of sides are parallel

52.

The missing reason is the same for steps 2 and 4. What is the missing reason?

a)

If alternate interior angles are congruent, then the lines are parallel.

b)

If vertical angles are congruent, then the lines are parallel.

c)

Definition of parallelogram

d)

Alternate interior angles formed by parallel lines are congruent.

53.

Choose the correct missing reasons for the proof.

a)

4) CPCTC; 6)All quads are parallelograms

b)

4) Alternate Interior Angles are congruent; 6) Definition of paralelogram

c)

4)CPCTC; 6)Definition of parallelogram

d)

4) Alternate Interior Angles are congruent; 6) All quads are parallelograms

54.

If you want to prove that Quadrilateral ABCD is a rectangle, what is the best piece of evidence to use?

a)

The lengths of AC and BD are the same, therefore AC and BD are congruent

b)

The slopes of AC and BD are the same, therefore AC and BD are congruent

c)

The slopes of AB and BD are the same, therefore AC is perpendicular to BD

d)

The slopes of AB and BD are opposite reciprocals, therefore AC is perpendicular to BD.

55.

If you wanted to prove that Quadrilateral ABCD is a rhombus, what would be the best piece of evidence to use?

a)

The length of each side is √(34), therefore all sides are congruent.

b)

The length of each side 8, therefore all sides are congruent.

c)

The slope of AC and BD is 5/3, therefore AC and BD are parallel.

d)

The slopes of the sides are opposite reciprocals, therefore opposite sides are parallel.

56.

If you wanted to prove that Quadrilateral ABCD is a Parallelogram, what would be the best piece of evidence to use?

a)

Length of AC = Length of BD, therefore Side AC is congruent to Side BD

b)

Length of AC = Length of BD, therefore Side AC is parallel to Side BD

c)

Slope of AC = Slope of BD, therefore Side AC is parallel to Side BD

d)

The Slopes of AC and BD are opposite reciprocals, therefore Side AC is parallel to Side BD

Geometry: Topic 6 (Quadrilaterals & Other Polygons)

Total questions: 56

Worksheet time: 2hrs 35mins

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