Unit Test Answers

Complete the proof to show that ABCD is a parallelogram. The slope of is The slope of is The slope of is The slope of is

A

lengths of consecutive sides are not equal

B

slopes of opposite sides are equal

C

lengths of opposite sides are equal

D

slopes of consecutive sides are not equal

1

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WXYZ is a trapezoid with WX ≅ YZ.

A

3 units

B

4 units

C

5 units

D

6 units

2

Rhombus LMNO is shown with its diagonals.

A

34°

B

45°

C

56°

D

68°

2

Parallelogram W X Y Z is shown. Diagonals are drawn from point W to point Y and from point Z to point X and intersect at point C. The length of W C is (x + 4) feet and the length of C Y is (2 x minus 7) feet.

A

11 ft

B

15 ft

C

21 ft

D

23 ft

3

A quadrilateral has congruent side lengths. 2 opposite angles have measures of 100 degrees. The other 2 opposite angles have measures of 70 degrees and (5 x) degrees.

A

14

B

15

C

16

D

17

3

Figure CDEF is a parallelogram.

A

2

B

3

C

4

D

5

4

If quadrilateral ABCD is an isosceles trapezoid, which statements must be true? Select three options

A

BC ∥ AD

B

BD ⊥ AC

C

BA ≅ CD

D

BE ≅ ED

E

∠CBA ≅ ∠BCD

4

A quadrilateral has congruent side lengths. 2 opposite angles have measures of 100 degrees. The other 2 opposite angles have measures of 70 degrees and (5 x) degrees.

A

14

B

15

C

16

D

17

5

Figure ABCD is a parallelogram.

A

6

B

7

C

8

D

9

5

A partial proof was constructed given that MNOP is a parallelogram. By the definition of a parallelogram,MN ∥ PO and MP ∥ NO.Using MP as a transversal, ∠M and ∠P are same-side interior angles, so they are supplementary.Using NO as a transversal, ∠N and ∠O are same-side interior angles, so they are supplementary.Using OP as a transversal, ∠O and ∠P are same-side interior angles, so they are supplementary.Therefore, __________________ because they are supplements of the same angle.

A

∠M is supplementary to ∠O

B

∠N is supplementary to ∠P

C

∠M ≅ ∠P

D

∠N ≅ ∠P

6

The perimeter of a square is 56 cm. What is the approximate length of its diagonal?

A

10.6 cm

B

14.0 cm

C

15.0 cm

D

19.8 cm

6

In parallelogram LMNO, MP = 21 m, LP = (y + 3) m, NP = (3y – 1) m, andOP = (2x – 1) m.

A

x = 10 m, y = 1 m

B

x = 10 m, y = 2 m

C

x = 11 m, y = 1 m

D

x = 11 m, y = 2 m

7

Trapezoid A B C D is shown. A diagonal is drawn from point B to point D. Sides B C and A D are parallel. Sides B A and C D are congruent. Angle C B D is 24 degrees and angle B A D is 116 degrees.

A

24°

B

40°

C

64°

D

92°

7

Kite FGHK is shown.

A

m=2

B

m=3

C

m=15

D

m=16

8

On a coordinate plane, triangle X Y Z is shown. Point X is at (1, 3), point Y is at (4, negative 1), and point Z is at (5, 6).

A

XZ is not perpendicular to XY

B

XZXY

C

The slope of XZ is , the slope of XY is , and XZ = XY = 5.

D

The slope of XZ is , the slope of XY is , and the slope of ZY = 7.

8

If quadrilateral ABCD is an isosceles trapezoid, which statements must be true? Select three options

A

BC ∥ AD

B

BD ⊥ AC

C

BA ≅ CD

D

BE ≅ ED

E

∠CBA ≅ ∠BCD

9

A partial proof was constructed given that MNOP is a parallelogram. By the definition of a parallelogram,MN ∥ PO and MP ∥ NO.Using MP as a transversal, ∠M and ∠P are same-side interior angles, so they are supplementary.Using NO as a transversal, ∠N and ∠O are same-side interior angles, so they are supplementary.Using OP as a transversal, ∠O and ∠P are same-side interior angles, so they are supplementary.Therefore, __________________ because they are supplements of the same angle.

A

∠M is supplementary to ∠O

B

∠N is supplementary to ∠P

C

∠M ≅ ∠P

D

∠N ≅ ∠P

9

On a coordinate plane, rectangle E F G H is shown. Point E is at (1, negative 1), point F is at (negative 4, 1), point G is at (negative 3, 4), and point H is at (2, 2).

A

+ units

B

+ units

C

22 units

D

39 units

10

In parallelogram LMNO, MP = 21 m, LP = (y + 3) m, NP = (3y – 1) m, andOP = (2x – 1) m.

A

x = 10 m, y = 1 m

B

x = 10 m, y = 2 m

C

x = 11 m, y = 1 m

D

x = 11 m, y = 2 m

10

Complete the proof to show that ABCD is a parallelogram. The slope of is The slope of is The slope of is The slope of is

A

lengths of consecutive sides are not equal

B

slopes of opposite sides are equal

C

lengths of opposite sides are equal

D

slopes of consecutive sides are not equal

11

Quadrilateral A B D C is shown.

A

AB ≅ CD

B

AC ≅ BD

C

AB ⊥ BD

D

CD ⊥ BD

11

EFGH is a rhombus.

A

6 units

B

8 units

C

10 units

D

14 units

12

WXYZ is a trapezoid with WX ≅ YZ.

A

3 units

B

4 units

C

5 units

D

6 units

12

ABCD is a square.

A

30°

B

45°

C

60°

D

90°

13

Parallelogram R S T U is shown. Angle S is 70 degrees.

A

m∠R = 70°, m∠T = 110°, m∠U = 110°

B

m∠R = 110°, m∠T = 110°, m∠U = 70°

C

m∠R = 110°, m∠T = 70°, m∠U = 110°

D

m∠R = 70°, m∠T = 110°, m∠U = 70°

13

On a coordinate plane, triangle X Y Z is shown. Point X is at (1, 3), point Y is at (4, negative 1), and point Z is at (5, 6).

A

XZ is not perpendicular to XY

B

XZXY

C

The slope of XZ is , the slope of XY is , and XZ = XY = 5.

D

The slope of XZ is , the slope of XY is , and the slope of ZY = 7.

14

Kite FGHK is shown.

A

m=2

B

m=3

C

m=15

D

m=16

14

Trapezoid A B C D is shown. A diagonal is drawn from point B to point D. Sides B C and A D are parallel. Sides B A and C D are congruent. Angle C B D is 24 degrees and angle B A D is 116 degrees.

A

24°

B

40°

C

64°

D

92°

15

In the parallelogram shown, AE = t + 2, CE = 3t − 14, and DE = 2t + 8.

A

20 units

B

24 units

C

48 units

D

68 units

15

Sofia cuts a piece of felt in the shape of a kite for an art project. The top two sides measure 20 cm each and the bottom two sides measure 13 cm each. One diagonal, EG, measures 24 cm.

A

5 cm

B

16 cm

C

21 cm

D

32 cm

16

EFGH is a rhombus.

A

6 units

B

8 units

C

10 units

D

14 units

16

Quadrilateral A B D C is shown.

A

AB ≅ CD

B

AC ≅ BD

C

AB ⊥ BD

D

CD ⊥ BD

17

The perimeter of a rhombus is 28 centimeters. What is the length of each side of the rhombus?

A

3 cm

B

4 cm

C

6 cm

D

7 cm

18

Parallelogram W X Y Z is shown. Diagonals are drawn from point W to point Y and from point Z to point X and intersect at point C. The length of W C is (x + 4) feet and the length of C Y is (2 x minus 7) feet.

A

11 ft

B

15 ft

C

21 ft

D

23 ft

18

Quadrilateral R S T Q is shown. Angle R is 132 degrees, angle Q is 56 degrees, and angle T is 79 degrees.

A

48o

B

56o

C

93o

D

101o

19

Figure CDEF is a parallelogram.

A

2

B

3

C

4

D

5

19

On a coordinate plane, parallelogram P Q R S is shown. Point P is at (negative 2, 5), point Q is at (2, 1), point R is at (1, negative 2), and point S is at (negative 3, 2).

A

units

B

+ units

C

units

D

+ 8 units

20

On a coordinate plane, rectangle E F G H is shown. Point E is at (1, negative 1), point F is at (negative 4, 1), point G is at (negative 3, 4), and point H is at (2, 2).

A

+ units

B

+ units

C

22 units

D

39 units

20

Parallelogram R S T U is shown. Angle S is 70 degrees.

A

m∠R = 70°, m∠T = 110°, m∠U = 110°

B

m∠R = 110°, m∠T = 110°, m∠U = 70°

C

m∠R = 110°, m∠T = 70°, m∠U = 110°

D

m∠R = 70°, m∠T = 110°, m∠U = 70°

21

Sofia cuts a piece of felt in the shape of a kite for an art project. The top two sides measure 20 cm each and the bottom two sides measure 13 cm each. One diagonal, EG, measures 24 cm.

A

5 cm

B

16 cm

C

21 cm

D

32 cm

21

Rhombus LMNO is shown with its diagonals.

A

34°

B

45°

C

56°

D

68°

22

ABCD is a square.

A

30°

B

45°

C

60°

D

90°

22

Figure ABCD is a parallelogram.

A

6

B

7

C

8

D

9

23

On a coordinate plane, parallelogram P Q R S is shown. Point P is at (negative 2, 5), point Q is at (2, 1), point R is at (1, negative 2), and point S is at (negative 3, 2).

A

units

B

+ units

C

units

D

+ 8 units

23

The perimeter of a square is 56 cm. What is the approximate length of its diagonal?

A

10.6 cm

B

14.0 cm

C

15.0 cm

D

19.8 cm

24

Quadrilateral R S T Q is shown. Angle R is 132 degrees, angle Q is 56 degrees, and angle T is 79 degrees.

A

48o

B

56o

C

93o

D

101o

24

In the parallelogram shown, AE = t + 2, CE = 3t − 14, and DE = 2t + 8.

A

20 units

B

24 units

C

48 units

D

68 units

25

A rectangle has a width of 9 units and a length of 40 units. What is the length of a diagonal?

A

31 units

B

39 units

C

41 units

D

49 units

25

Figure PQRS is a parallelogram. The expressions represent the measures of the angles in degrees.

A

5

B

10

C

20

D

25

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