Answers CR CCSS Math 2 S2 M2960OXParallelograms

Parallelograms — Test Answers

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Given: RT ≅ TV and ST ≅ TUProve: RSVU is a parallelogram. Statements Reasons1.RT ≅ TV; ST ≅ TU1.given2.∠RTS and ∠VTU are vert. ∠s;∠RTU and ∠VTS are vert. ∠s2.definition of vertical angles3.∠RTS ≅ ∠VTU;∠RTU ≅ ∠VTS3.vertical angles are congruent4.?4.SAS congruency theorem5.∠VRS ≅ ∠RVU; ∠USR ≅ ∠SUV; ∠VRU ≅ ∠RVS; ∠RUS ≅ ∠USV5.CPCTC6.∠VRS and ∠RVU, ∠USR and ∠SUV, ∠VRU and ∠RVS, ∠RUS and ∠USV are each a pair of alternate interior angles6.definition of alternate interior angles7.RS ∥ UV and RU ∥ SV7.converse of the parallelogram diagonal theorem8.RSVU is a parallelogram8.definition of parallelogramWhat is the missing statement in step 4?

△RTS ≅ △VTU and △RTU ≅ △VTS

△RTS ≅ △RVS and △RTU ≅ △STV

△VRS ≅ △VRU and △USR ≅ △USV

△VUR ≅ △VUS and △UVS ≅ △SRU

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In the rhombus, . What is the measure of ?

Answer not available

The angle measures of quadrilateral RSTU are shown.m∠R = (2x)°m∠S = (3x – 35)°m∠T = (x + 35)°

Yes, opposite angles R and T are congruent to each other if x = 35.

Yes, consecutive angles R and S are congruent to each other if x = 35.

No, if x = 35, all three given angles measure 70°. The fourth angle would measure 150°.

No, if x = 35, the three given angle measures make it impossible for the figure to be a quadrilateral.

Which statements are true about the kite? Check all that apply.

This polygon is a quadrilateral.

This polygon has four right angles.

This polygon has two pairs of congruent sides.

This polygon has opposite sides that are congruent.

This polygon has one set of opposite angles that are congruent.

This polygon has two sets of opposite angles that are congruent.

In parallelogram RSTU, SW = 4 cm, WT = 6 cm, RS = 5 cm, and ST = 7 cm.

4 cm

5 cm

6 cm

7 cm

Which explains whether or not a parallelogram can be classified as a rectangle?

A parallelogram is also a rectangle. Both quadrilaterals have four right angles.

A parallelogram is also a rectangle. Both quadrilaterals have opposite sides that are congruent, opposite sides that are parallel, and four congruent angles.

A parallelogram is not a rectangle. A rectangle has opposite sides that are congruent, and a parallelogram does not.

A parallelogram is not a rectangle. A rectangle must have four right angles, and a parallelogram must only have opposite angles congruent.

Figure ABCD is a parallelogram.

An interior angle of a regular polygon has a measure of 108°. What type of polygon is it?

pentagon

hexagon

octagon

nonagon

In parallelogram WXYZ, WY = 12 in., XZ = 16 in., WX = 10 in., and XY = 9 in.

6 in.

7 in.

8 in.

9 in.

A 15-meter by 23-meter garden is divided into two sections. Two sidewalks run along the diagonal of the square section and along the diagonal of the smaller rectangular section.

21.2 m

27.5 m

32.5 m

38.2 m

Parallelogram L M N O is shown. Angle N is (2 x) degrees and angle L is (3 x minus 20) degrees.

20°

30°

40°

50°

Jacob is cutting a tile in the shape of a parallelogram. Two opposite angles have measures of (6n − 70)° and (2n + 10)°.What are the two different angle measures of the parallelogram-shaped tile?

20° and 160°

50° and 130°

30° and 150°

70° and 110°

What is the measure of each exterior angle of a regular hexagon?

40°

45°

60°

72°

Four interior angles of a pentagon measure 88°, 118°, 132°, and 100°. What is the measure of the fifth interior angle?

82°

92°

102°

112°

Juanita is cutting a piece of construction paper in the shape of a parallelogram. Two opposite sides of the parallelogram have lengths (5n − 6) cm and (3n − 2) cm. A third side measures (2n + 3) cm.What are the lengths of two adjacent sides of the parallelogram?

2 cm and 2 cm

4 cm and 7 cm

7 cm and 9 cm

13 cm and 19 cm

Which polygon is a convex heptagon?

A polygon has 7 sides. No angles go inside of the shape.