AnswersCR CCSS Math 2 S2 M2960OXProving a Quadrilateral Is a Parallelogram

Special Parallelograms Answers

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1
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ABCD is a square.

Question illustration
A
5 units
B
7 units
C
11 units
D
13 units
2
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The figure is a parallelogram. One diagonal measures 28 units.

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A
No, it is not a rectangle because the diagonals are congruent.
B
No, it is not a rectangle because the sides of the parallelogram do not meet at right angles.
C
Yes, it is a rectangle because the diagonals are congruent.
D
Yes, it is a rectangle because the sides of the parallelogram do meet at right angles.
3

Which measures are true for the quilt piece? Select three options.

A
a = 60°
B
x = 3 in.
C
The perimeter of the rhombus is 16 inches.
D
The measure of the greater interior angle of the rhombus is 90°.
E
The length of the longer diagonal is approximately 7 inches.
4

Which statements are true of all squares? Select three options.The diagonals are perpendicular.The diagonals are congruent to each other.The diagonals bisect the vertex angles.The diagonals are congruent to the sides of the square.The diagonals are twice the length of one side of the square.

A
The diagonals are perpendicular.
B
The diagonals are congruent to each other.
C
The diagonals bisect the vertex angles.
D
The diagonals are congruent to the sides of the square.
E
The diagonals are twice the length of one side of the square.
5

A square stained glass window is divided into four congruent triangular sections by iron edging to represent the seasons of the year. Each diagonal of the square window measures 9 inches.

Question illustration
A
43.5 inches
B
50.9 inches
C
54.0 inches
D
61.5 inches
6

Diagonals AC and BD form right angles at point M in parallelogram ABCD. Prove ABCD is a rhombus. Statements Reasons1.ABCD is a parallelogram1.given2.∠AMB, ∠BMC, ∠CMD, and ∠DMA are right angles2.given3.∠AMB ≅ ∠BMC ≅ ∠CMD ≅ ∠DMA3.right angles are congruent4.AC bisects BD; BD bisects AC;4.diagonals of a parallelogram bisect each other5.AM ≅ MC, MB ≅ MD5.definition of a bisector6.?6.SAS congruency theorem7.AB ≅ BC ≅ CD ≅ DA7.CPCTC8.figure ABCD is a rhombus8.definition of a rhombus

Question illustration
A
△ABC ≅ △ADC ≅ △BAD ≅ △BCD
B
△AMB ≅ △CMB ≅ △CMD ≅ △AMD
C
△ABC ≅ △ADC ≅ △AMD ≅ △BMC
D
△AMB ≅ △CMD ≅ △BAD ≅ △BCD
7

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
8

The figure shown is a rhombus.

Question illustration
A
x + y = z
B
2x = y + z
C
z + x = 2y
D
2x + 2y = 4z
9

Consider the diagram and proof below.Given: WXYZ is a parallelogram, ZX ≅ WYProve: WXYZ is a rectangle Statement Reason1.WXYZ is a ▱; ZX ≅ WY1.given2.ZY ≅ WX2.opp. sides of ▱ are ≅3.YX ≅ YX3.reflexive4.△ZYX ≅ △WXY4.SSS ≅ thm.5.∠ZYX ≅ ∠WXY5.CPCTC6.m∠ZYX ≅ m∠WXY6.def. of ≅7.m∠ZYX + m∠WXY = 180°7.?8.m∠ZYX + m∠ZYX = 180°8.substitution9.2(m∠ZYX) = 180°9.simplification10.m∠ZYX = 90°10.div. prop. of equality11.WXYZ is a rectangle11.rectangle ∠ thm.What is the missing reason in Step 7?

Question illustration
A
triangle angle sum theorem
B
quadrilateral angle sum theorem
C
definition of complementary
D
consecutive ∠s in a ▱ are supplementary
10

Rectangle T R E C is shown. Diagonals are drawn from point R to point C and from point E to point T and intersect in the middle. The distance from point R to the middle is 2 x minus 3 and the distance from the middle point to point C is x + 7.

Question illustration
A
10 units
B
17 units
C
20 units
D
34 units
11

Rectangle PQRS is shown with its diagonals, PR and QS.

Question illustration
A
right triangle
B
equilateral triangle
C
isosceles triangle
D
scalene triangle
12

A square with diagonals is shown. The distance from one point to the middle point is 3. The length from the center point to another point is 3.

Question illustration
A
3.0 units
B
3.5 units
C
4.2 units
D
4.9 units
13

Figure ABCD is a parallelogram.

Question illustration
A
13
B
15
C
18
D
23
14

A rectangle is shown. All angles are right angles. The length of one side is 2 x and the length of another side is 3 x + 3.

Question illustration
A
14 units
B
28 units
C
33 units
D
45 units
15

The perimeter of square JKLM is 48 units.

Question illustration
A
6
B
9
C
12
D
15
16

A square with diagonals is shown. The distance from one point to the middle point is x. The length from the center point to another point is x. The length of a side is 8.

Question illustration
A
2.8 units
B
3.3 units
C
4.0 units
D
5.7 units
17

Rhombus LMNO is shown with its diagonals.

Question illustration
A
7 cm
B
9 cm
C
14 cm
D
21 cm

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