Free Printable Geometry: Topic 6 (Quadrilateral & Polygons)

1.

Find the measure of the angle x.

a)

105

b)

115

c)

65

d)

75

2.

What is the value of x?

a)

4

b)

360

c)

12

d)

6

3.

The figure is a parallelogram.
Solve for x.

a)

1

b)

11

c)

7

d)

6

4.

Find the missing angle.

a)

75°

b)

85°

c)

100°

d)

45°

5.

What is the value of x?

(a)

6.

What must m∠XWZ be for WXYZ to be a parallelogram?

a)

62

b)

118

c)

38

d)

not enough information

7.

What must the values of m and n be for WXYZ to be a parallelogram?

a)

m = 4, n = 5

b)

m = 2, n = 7

c)

m = 18, n = 13

d)

not enough information

8.

The diagonals of parallelogram PQRS intersect at Z. Which statement must be true?

a)

$\overline{QZ}\ \cong\overline{SZ}$

b)

$\overline{QS}\ \perp\ \overline{RP}$

c)

$\angle QZR\ \cong\angle QZP$

d)

$\angle QRP\ \cong\ \angle SRP$

9.

What is the measure of an interior angle of a regular 15-gon?

a)

$135\degree$

b)

$54\degree$

c)

$156\degree$

d)

$24\degree$

10.

A polygon has ____ sides when each exterior angle measures 22.5˚.

a)

12

b)

18

c)

16

d)

14

11.

WXYZ is shown. What is m∠XWZ?

a)

115

b)

52

c)

65

d)

Not enough information

12.

Solve for x

a)

45

b)

12

c)

90

d)

2

13.

The diagonals of a parallelogram always ...

a)

are congruent

b)

are perpendicular

c)

bisect each other

d)

are parallel

14.

In a parallelogram, opposite angles are ________.

a)

congruent

b)

supplementary

c)

consecutive

d)

parallel

15.

The figure is a parallelogram.

Find x and y.

a)

x = 70, y = 80

b)

x = 70, y = 30

c)

x = 80, y = 70

d)

x = 80, y = 30

16.

The figure is a parallelogram.

Find x and y.

a)

x = 30, y = 40

b)

x = 40, y = 30

c)

x = 40, y = 15

d)

x = 30, y = 30

17.

The figure is a parallelogram.

Solve for x and y.

a)

x = 9, y = 4

b)

x = 6, y = 4

c)

x = 6, y = 2

d)

x = 4, y = 2

18.

Is the quadrilateral a parallelogram? If yes, state how you know.

a)

Parallelogram Opposite Sides Converse

b)

Definition of Parallelogram

c)

Parallelogram Diagonals Converse

d)

Not enough info

19.

Is the quadrilateral a parallelogram? If yes, state how you know.

a)

Definition of Parallelogram

b)

Parallelogram Opposite Angles Converse

c)

Opposite Sides Parallel and Congruent Theorem

d)

Not enough info

20.

The figure is a parallelogram.
Solve for x.

a)

12

b)

4

c)

6

d)

2

21.

Which of the following are properties of parallelograms?

(Select ALL that apply)

a)

Two pairs of sides are parallel

b)

Opposite sides are congruent

c)

Diagonals are congruent

d)

Diagonals bisect each other

e)

Opposite angles are supplementary

22.

Which is NOT a property of a parallelogram?

a)

Diagonals bisect each other

b)

Diagonals are congruent

c)

Both pairs of opposite sides are parallel

d)

Both pairs of opposite angles are congruent

23.

In a parallelogram, consecutive angles are __________.

a)

congruent

b)

supplementary

c)

corresponding

d)

parallel

24.

In a parallelogram, diagonals are __________.

a)

perpendicular

b)

bisected

c)

congruent

d)

parallel

25.

WXYZ is a parallelogram. Find XW

a)

cannot be determined

b)

3

c)

11

d)

24

26.

Define parallelogram

a)

a quadrilateral with exactly one pair of parallel sides

b)

multiple quadrilaterals with 4 congruent sides

c)

a polygon with opposite sides parallel and congruent

d)

a quadrilateral with 4 right angles and opposite sides are congruent

27.

Which of the following statements is false?

a)

BD and AC are perpendicular

b)

BD and AC are congruent

c)

∠A and ∠C are congruent

d)

BD bisects AC

28.

Solve for Angle 1 and Angle 2.

a)

1= 92, 2 = 46 degrees

b)

1 = 118, 2 = 118 degrees

c)

1 = 92, 2 = 92

d)

1 = 136, 2 = 100

29.

The diagonals in a kite __________.

a)

are perpendicular

b)

are congruent

c)

bisect each other

30.

What is the value of x, y and z on the kite.

a)

x=90

y=57

z=57

b)

x=90

y=33

z=57

c)

x=180

y=57

z=33

d)

x=33

y=57

z=90

31.

What is the value of x on the kite.

a)

3

b)

15

c)

13

d)

23

32.

The diagonals in a kite __________.

a)

are perpendicular

b)

are congruent

c)

bisect each other

33.

Base angles of an isosceles trapezoid are _____.

a)

neither

b)

supplementary

c)

congruent

34.

The legs of an isosceles trapezoid are _____.

a)

parallel

b)

perpendicular

c)

congruent

d)

skew

35.

Which of the following statements is false?

a)

all four angles are congruent

b)

the legs are congruent

c)

the diagonals are congruent

d)

the base angles are congruent

36.

Find the measure of ∠K:

a)

114°

b)

124°

c)

77°

d)

66°

37.

A midsegment of a trapezoid

a)

is the same as a diagonal

b)

is half the sum of the lengths of the bases

c)

is parallel to the legs

d)

none of these

38.

Find the value of x.

a)

4

b)

6

c)

5

d)

129

39.

Determine the value of x that would classify this quadrilateral as a parallelogram. (The expression are for the tick marks on the diagram).

a)

x = 8

b)

x = 26

c)

x = 28

d)

x = 38

40.

Find m∠FHJ

a)

70

b)

82

c)

152

d)

28

41.

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

42.

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

43.

Which theorem shows that the quadrilateral is a parallelogram?

a)

Parallelogram Diagonals Converse

b)

Parallelogram Opposite Sides Converse

c)

Parallelogram Opposite Angles Converse

d)

Opposite Sides Parallel and Congruent Theorem

44.

Find the values of x and y that make the quadrilateral a parallelogram.

a)

x = 4, y = 3

b)

x = 3, y = -2

c)

x = 1, y = 4

d)

x = 3, y = 4

45.

Find the values of x and y that make the quadrilateral a parallelogram.

a)

x = 3, y = 2

b)

x = 25, y = 15

c)

x = 15, y = 25

d)

x = 113, y = 67

46.

Given Rhombus TUVW. Find m∠2.

a)

62

b)

28

c)

90

d)

78

47.

Given Rhombus TUVW. Find m∠4.

a)

62

b)

28

c)

90

d)

78

48.

The diagonals of a rectangle are

a)

parallel

b)

congruent

c)

perpendicular

d)

not congruent

49.

A square has all the properties of a

a)

parallelogram

b)

rectangle

c)

rhombus

d)

parallelogram, rectangle, and rhombus

50.

If the figure is a rectangle, the value of x is...

a)

2

b)

12

c)

13

d)

28

51.

Find the missing angle of the trapezoid.

a)

65

b)

115

c)

180

d)

None of these

52.

In a parallelogram, consecutive angles are __________.

a)

congruent

b)

supplementary

c)

corresponding

d)

parallel

53.

Rectangles and squares both have ______________.

a)

all congruent sides

b)

four right angles

c)

perpendicular diagonals

d)

feelings

54.

Which of the following quadrilaterals have 2 pairs of parallel sides? Choose ALL possible answers.

a)

trapezoid

b)

parallelogram

c)

square

d)

kite

e)

rhombus

55.

A trapezoid has two congruent sides

a)

sometimes

b)

always

c)

never

56.

a)

90

b)

23

c)

22

d)

180

57.

Base angles of an isosceles trapezoid are _____.

a)

neither

b)

supplementary

c)

congruent

58.

Find the measure of ∠K:

a)

114°

b)

124°

c)

77°

d)

66°

59.

Find Angle 1, Angle 2, and Angle 3.

a)

Angle 1 = 45, Angle 2 = 45, Angle 3 = 135

b)

Angle 1 = 135, Angle 2 = 55, Angle 3 = 55

c)

Angle 1 = 55, Angle 2 = 55, Angle 3 = 125

d)

Angle 1 = 40, Angle 2 = 40, Angle 3 = 135

60.

Check all that apply to the DIAGONALS of a RHOMBUS

a)

diagonals bisect (split in half) each other

b)

diagonals are congruent

c)

diagonals bisect (split in half) opposite angles

d)

diagonals are perpendicular (intersect in a 90^o angle)

61.

Check all that apply to the DIAGONALS of a SQUARE

a)

diagonals bisect (split in half) each other

b)

diagonals are congruent

c)

diagonals bisect (split in half) opposite angles

d)

diagonals are perpendicular (intersect in a 90^o angle)

62.

$Find\ the\ measure\ of\ \angle F$

a)

120

b)

24

c)

60

d)

180

63.

Which type of quadrilateral has the properties:

1) Consecutive sides are congruent.

2) Consecutive sides are perpendicular.

a)

Rhombus

b)

Rectangle

c)

Square

d)

Kite

64.

Find the length of $\overline{BC}$

a)

24

b)

10

c)

32

d)

30

65.

Find the length of

\overline{EC}

(a)

66.

Which is a property common to all parallelograms?

a)

congruent diagonals

b)

diagonals bisect opposite angles

c)

diagonals are perpendicular

d)

diagonals bisect each other

67.

Which statements are true about kites?

a)

Opposite sides are parallel

b)

Diagonals are perpendicular

c)

2 sets of congruent sides

d)

One diagonal is bisected

e)

consecutive angles are supplementary

68.

A rhombus is a parallelogram with

a)

four congruent sides

b)

four congruent diagonals

c)

four acute angles

d)

four congruent angles

69.

The diagonals of a rhombus are

a)

parallel

b)

congruent

c)

perpendicular

d)

equal to the side lengths

70.

Given Rhombus TUVW. Find m∠2.

a)

62

b)

28

c)

90

d)

78

71.

Given Rhombus TUVW. Find m∠4.

a)

62

b)

28

c)

90

d)

78

72.

The figure is a rhombus.
Solve for x.

a)

1

b)

11

c)

7

d)

6

73.

If m∠B is 54° what is the m∠CDB?

a)

54°

b)

27°

c)

108°

d)

36°

74.

True/False: Every rhombus is a square.

a)

True - they both have 4 equal sides

b)

True - the diagonals are perpendicular

c)

False - a rhombus CAN'T have 90 degree angles

d)

False - a rhombus won't always have 90 degree angles.

75.

Find y.

a)

2

b)

4

c)

15

d)

10

76.

If BA=5x+5 and AD=10x-20, find BD.

a)

60

b)

30

c)

5

d)

10

77.

Find the value of x if m∠CDA = 9x+3 and m∠EDA = 6x+15.

a)

39

b)

4

c)

4.8

d)

-4

78.

Solve for the variables.

a)

m=68, n=70

b)

m=35, n=70

c)

m=35, n=110

d)

m=68, n=110

79.

Norman drew three points on a coordinate grid, as shown. If Norman draws a fourth point to form a parallelogram , which point could not be Norman's point ?

a)

( 5,5 )

b)

( 1,-1 )

c)

( -1,3 )

d)

( 2, -2 )

80.

In the coordinate plane, $J\left(2,3\right)$ , $K\left(10,4\right)$ and $L\left(6,10\right)$ .

What is the best classification of $\triangle JKL$ ?

a)

equilateral

b)

isoceles

c)

rectangle

d)

scalene

81.

In the coordinate plane, A(–5, 0), B(2, –6), C(8, 1), and D(1, 7). Then ABCD is a rectangle because :

a)

The slopes of $\overline{AB}$ and $\overline{CD}$ are equal

b)

The slopes of $\overline{AD}$ and $\overline{BC}$ are equal

c)

Both answers at the same time.

82.

Calculate the slopes of the diagonals then choose the right answer.

a)

$\frac{2}{3}$ and $2$

b)

$-\frac{3}{2}$ and $\frac{2}{3}$

c)

$\frac{3}{2}$ and $\frac{2}{3}$

d)

$\frac{3}{2}$ and $-\frac{2}{3}$

83.

Draw a quadrilateral with vertices $\left(5,3\right)$ , $\left(5,-1\right)$ , $\left(-1,3\right)$ and $\left(-1,-1\right)$ .

What special quadrilateral is formed by connecting the MIDPOINTS of the sides?

a)

kite

b)

rectangle

c)

trapezoid

d)

rhombus

84.

Let $T\left(1,1\right)$ , $V\left(9,2\right)$ and $S\left(5,8\right)$ .

Is $\Delta TVS$ scalene, isosceles, or equilateral?

a)

cannot be determined

b)

scalene

c)

isosceles

d)

equilateral

85.

A polygon can have curved sides.

a)

True

b)

False

Geometry: Topic 6 (Quadrilateral & Polygons)

Total questions: 85

Worksheet time: 4hrs 16mins

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