Trapezoids and Kites Answers

Which statements are correct regarding the properties of trapezoids? Check all that apply.The diagonals of an isosceles trapezoid are congruent.The bases of a trapezoid are parallel.The adjacent sides of a trapezoid are congruent.Base angles of a trapezoid are congruent.The diagonals of a trapezoid are perpendicular.

A

The diagonals of an isosceles trapezoid are congruent.

B

The bases of a trapezoid are parallel.

C

The adjacent sides of a trapezoid are congruent.

D

Base angles of a trapezoid are congruent.

E

The diagonals of a trapezoid are perpendicular.

1

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What is the length of the sides of kite ABCD?

A

AB = 20; CD = 15

B

AB = 15; CD = 20

C

AB = 9; CD = 16

D

AB = 24; CD = 25

1

Charlene puts together two isosceles triangles so that they share a base, creating a kite. The legs of the triangles are 10 inches and 17 inches, respectively. If the length of the base for both triangles is 16 inches long, what is the length of the kite’s other diagonal?

A

6 inches

B

inches

C

inches

D

21 inches

1

Which statements are correct regarding the properties of trapezoids? Check all that apply.The diagonals of an isosceles trapezoid are congruent.The bases of a trapezoid are parallel.The adjacent sides of a trapezoid are congruent.Base angles of a trapezoid are congruent.The diagonals of a trapezoid are perpendicular.

A

The diagonals of an isosceles trapezoid are congruent.

B

The bases of a trapezoid are parallel.

C

The adjacent sides of a trapezoid are congruent.

D

Base angles of a trapezoid are congruent.

E

The diagonals of a trapezoid are perpendicular.

1

What is the length of the sides of kite ABCD?

A

AB = 20; CD = 15

B

AB = 15; CD = 20

C

AB = 9; CD = 16

D

AB = 24; CD = 25

1

What information would verify that LMNO is an isosceles trapezoid? Check all that apply.

A

LN ≅ MO

B

LM ≅ ON

C

LO ≅ MN

D

∠L ≅ ∠N

E

∠L ≅ ∠M

1

What are the values of a and b?

A

a = 4; b = 10

B

a = 4; b = 40

C

a = 8; b = 10

D

a = 8; b = 40

1

Charlene puts together two isosceles triangles so that they share a base, creating a kite. The legs of the triangles are 10 inches and 17 inches, respectively. If the length of the base for both triangles is 16 inches long, what is the length of the kite’s other diagonal?

A

6 inches

B

inches

C

inches

D

21 inches

1

22.632.6292.6✔ 112.6

Answers:

If the measure of angle BCD is 67.4°, the measure of angle ABC is °.:112.6

If the length of base AB is 80 feet, the length of DC is feet.:105

1

congruent✔ isosceles trapezoidcongruent triangles

Answers:

It is given that trapezoid EFGH is an isosceles trapezoid. We know that FE ≅ GH by the definition of . The base angle theorem of isosceles trapezoids verifies that angle is congruent to angle . We als:isosceles trapezoid

It is given that trapezoid EFGH is an isosceles trapezoid. We know that FE ≅ GH by the definition of . The base angle theorem of isosceles trapezoids verifies that angle is congruent to angle . We als:FEH

It is given that trapezoid EFGH is an isosceles trapezoid. We know that FE ≅ GH by the definition of . The base angle theorem of isosceles trapezoids verifies that angle is congruent to angle . We als:GHE

It is given that trapezoid EFGH is an isosceles trapezoid. We know that FE ≅ GH by the definition of . The base angle theorem of isosceles trapezoids verifies that angle is congruent to angle . We als:reflexive

It is given that trapezoid EFGH is an isosceles trapezoid. We know that FE ≅ GH by the definition of . The base angle theorem of isosceles trapezoids verifies that angle is congruent to angle . We als:SAS

2

✔ 153062118

A

✔ 15

B

30

C

62

D

118

2

2580✔ 10585

A

25

B

80

C

✔ 105

D

85

2

✔ FEHFEGFHE

A

✔ FEH

B

FEG

C

FHE

3

HE✔ GHEHEG

A

HE

B

✔ GHE

C

HEG

4

congruency✔ reflexivesubstitution

A

congruency

B

✔ reflexive

C

substitution

5

AASSSS✔ SAS

A

AAS

B

SSS

C

✔ SAS

116446

Use the diagram to find the missing measures.

Answers:

The measure of angle GHE is °.:62

The length of GE is .:15

116446

Use the diagram to find the missing measures.

Answers:

The measure of angle GHE is °.:62

The length of GE is .:15

116446

Use the diagram to find the missing measures.

Answers:

The measure of angle GHE is °.:62

The length of GE is .:15

116447

✔ 15X 3062118

A

✔ 15

B

X 30

C

62

D

118

116470

22.632.6292.6✔ 112.6

Answers:

If the measure of angle BCD is 67.4°, the measure of angle ABC is °.:112.6

If the length of base AB is 80 feet, the length of DC is feet.:105

116476

congruent✔ isosceles trapezoidcongruent triangles

Answers:

It is given that trapezoid EFGH is an isosceles trapezoid. We know that FE ≅ GH by the definition of . The base angle theorem of isosceles trapezoids verifies that angle is congruent to angle . We als:FEH

It is given that trapezoid EFGH is an isosceles trapezoid. We know that FE ≅ GH by the definition of . The base angle theorem of isosceles trapezoids verifies that angle is congruent to angle . We als:GHE

It is given that trapezoid EFGH is an isosceles trapezoid. We know that FE ≅ GH by the definition of . The base angle theorem of isosceles trapezoids verifies that angle is congruent to angle . We als:reflexive

It is given that trapezoid EFGH is an isosceles trapezoid. We know that FE ≅ GH by the definition of . The base angle theorem of isosceles trapezoids verifies that angle is congruent to angle . We als:SAS

116481

✔ kitecongruentquadrilateral

Answers:

It is given that quadrilateral ABCD is a kite. We know that AD ≅ CD by the definition of . By the kite diagonal theorem, AC is to BD This means that angles AED and CED are right angles. We also see th:kite

It is given that quadrilateral ABCD is a kite. We know that AD ≅ CD by the definition of . By the kite diagonal theorem, AC is to BD This means that angles AED and CED are right angles. We also see th:perpendicular

It is given that quadrilateral ABCD is a kite. We know that AD ≅ CD by the definition of . By the kite diagonal theorem, AC is to BD This means that angles AED and CED are right angles. We also see th:reflexive

It is given that quadrilateral ABCD is a kite. We know that AD ≅ CD by the definition of . By the kite diagonal theorem, AC is to BD This means that angles AED and CED are right angles. We also see th:HL

116481

✔ kitecongruentquadrilateral

Answers:

It is given that quadrilateral ABCD is a kite. We know that AD ≅ CD by the definition of . By the kite diagonal theorem, AC is to BD This means that angles AED and CED are right angles. We also see th:kite

It is given that quadrilateral ABCD is a kite. We know that AD ≅ CD by the definition of . By the kite diagonal theorem, AC is to BD This means that angles AED and CED are right angles. We also see th:perpendicular

It is given that quadrilateral ABCD is a kite. We know that AD ≅ CD by the definition of . By the kite diagonal theorem, AC is to BD This means that angles AED and CED are right angles. We also see th:reflexive

It is given that quadrilateral ABCD is a kite. We know that AD ≅ CD by the definition of . By the kite diagonal theorem, AC is to BD This means that angles AED and CED are right angles. We also see th:HL

116482

congruentparallel✔ perpendicular

A

congruent

B

parallel

C

✔ perpendicular

116483

congruency✔ reflexivesubstitution

A

congruency

B

✔ reflexive

C

substitution

116484

AAS✔ HLSAS

A

AAS

B

✔ HL

C

SAS

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