AnswersCR CCSS Math 2 S2 M2960OXParallelograms

4.4 - Volume of Pyramids Answers

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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
2
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Rhombus LMNO is shown with its diagonals.

Question illustration
A
7 cm
B
9 cm
C
14 cm
D
21 cm
3

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
4

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
5

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

Question illustration
A
right triangle
B
equilateral triangle
C
isosceles triangle
D
scalene triangle
6

The figure shown is a rhombus.

Question illustration
A
x + y = z
B
2x = y + z
C
z + x = 2y
D
2x + 2y = 4z
7

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
8

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
9

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
10

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.
11

The figure is a parallelogram. One diagonal measures 28 units.

Question illustration
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.
12

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

Question illustration
A
right triangle
B
equilateral triangle
C
isosceles triangle
D
scalene triangle
13

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
14

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
15

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
16

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.
17

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
18

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
19

ABCD is a square.

Question illustration
A
5 units
B
7 units
C
11 units
D
13 units
20

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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