Answers Summer 2026 CC GEOMETRY A MiderosParallelograms

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.

2.8 units

3.3 units

4.0 units

5.7 units

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

No, it is not a rectangle because the diagonals are congruent.

No, it is not a rectangle because the sides of the parallelogram do not meet at right angles.

Yes, it is a rectangle because the diagonals are congruent.

Yes, it is a rectangle because the sides of the parallelogram do meet at right angles.

Rhombus LMNO is shown with its diagonals.

7 cm

9 cm

14 cm

21 cm

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

right triangle

equilateral triangle

isosceles triangle

scalene triangle

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

31 units

39 units

41 units

49 units

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.

3.0 units

3.5 units

4.2 units

4.9 units

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.

10 units

17 units

20 units

34 units

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.

2.8 units

3.3 units

4.0 units

5.7 units

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

right triangle

equilateral triangle

isosceles triangle

scalene triangle

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.

43.5 inches

50.9 inches

54.0 inches

61.5 inches

The figure shown is a rhombus.

x + y = z

2x = y + z

z + x = 2y

2x + 2y = 4z

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

a = 60°

x = 3 in.

The perimeter of the rhombus is 16 inches.

The measure of the greater interior angle of the rhombus is 90°.

The length of the longer diagonal is approximately 7 inches.

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

△ABC ≅ △ADC ≅ △BAD ≅ △BCD

△AMB ≅ △CMB ≅ △CMD ≅ △AMD

△ABC ≅ △ADC ≅ △AMD ≅ △BMC

△AMB ≅ △CMD ≅ △BAD ≅ △BCD

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?

triangle angle sum theorem

quadrilateral angle sum theorem

definition of complementary

consecutive ∠s in a ▱ are supplementary

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.

14 units

28 units

33 units

45 units