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Quadrilaterals: Trapezoids and Kites Do Now: Quick 5-minute Quiz 1

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Quadrilaterals: Trapezoids and Kites

Do Now: Quick 5-minute Quiz

1

Kites

2.) Draw a kite and the diagonals of the kite.

3.) What additional properties do kites have?

1.) Definition of a kite:

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Properties of Kites1.) Has two sets of ______________ ___________ sides.

2.) _______________ angles are ____________.

3.) ____________ angles are ________________.

4.) Diagonals are ________________.

5.) The diagonal from the vertex angles ___________ the other diagonal.

6.) Diagonals from the __________ angles __________ the ___________ angles.

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Proof Non-Vertex Angles of a Kite are Congruent.

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Proof: Diagonal Connecting Vertex Angles Bisects the Vertex Angles.

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Parts of a Trapezoid1.) Bases:

2.) Legs:

3.) Base Angles:

4.) Isosceles Trapezoid:

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Trapezoid

2.) Draw an isosceles trapezoid and the diagonals.

3.) What additional properties do isosceles trapezoids have?

1.) Definition of a trapezoid:

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Properties of Isosceles Trapezoids1.) Legs are _____________.

2.) Bases are ______________.

3.) ____________ angles are ________________.

4.) Diagonals are ________________.

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Proof of Congruent Diagonals in an Isosceles Trapezoid (Given Base Angles are Congruent)

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Home Work

Chapter 8 ! Skills Practice 623

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Skills Practice Skills Practice for Lesson 8.3

Name _____________________________________________ Date ____________________

Kites and Trapezoids Properties of Kites and Trapezoids

VocabularyWrite the term from the box that best completes each statement.

base angles of a trapezoid biconditional statement isosceles trapezoid

1. The are either pair of angles of a trapezoid that share a base as a common side.

2. A(n) is a trapezoid with congruent non-parallel sides.

3. A(n) is a statement that contains if and only if.

Problem SetComplete each statement for kite PRSQ.

1. ___

PQ ! ___

QS and ___

PR ! ___

SR

QR

S

T

P

2. !QPR ! !

3. ___

PT !

4. !PQT ! ! and !PRT ! !

624 Chapter 8 ! Skills Practice

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8Complete each statement for trapezoid UVWX.

5. The bases are ___

UV and ____

WX .

X

U V

W

6. The pairs of base angles are ! and ! , and ! and ! .

7. The legs are and .

8. The vertices are , , , and .

Construct each quadrilateral using the given information.

9. Construct kite QRST with diagonals ___

QS and ___

RT intersecting at point M.

Q S

R T

Q

T M

S

R

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Chapter 8 ! Skills Practice 627

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Name _____________________________________________ Date ____________________

Use the given figure to answer each question.

15. The figure shown is a kite with !DAB ! !DCB. Which sides of the kite are congruent?

A

B

D C

___

AB and ___

CB are congruent.

___

AD and ___

CD are congruent.

16. The figure shown is a kite with ___

FG ! ___

FE . Which of the kite’s angles are congruent?

E

F

G H

17. Given that IJLK is a kite, what kind of triangles are formed by diagonal __

IL ?

I J

K

L

Chapter 8 ! Skills Practice 629

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Name _____________________________________________ Date ____________________

Use the given figure to answer each question.

21. The figure shown is an isosceles trapezoid with ___

AB || ___

CD . Which sides are congruent?

A B

C D

___

AC and ___

BD are congruent.

22. The figure shown is an isosceles trapezoid with ___

EH ! ___

FG . Which sides are parallel?

E F

H G

23. The figure shown is an isosceles trapezoid with __

IJ ! ___

KL . What are the bases?

I

J

K

L

24. The figure shown is an isosceles trapezoid with ____

MP ! ___

NO . What are the pairs of base angles?

PM

NO

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142 Chapter 8 ! Assignments

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8Quadrilateral WXYZ is an isosceles trapezoid.

YX

ZW

V

5. If m!XWZ ! 66°, what is m!YZW? Explain.

6. If the length of ____

WY is 10 inches, what is ZX? Explain.

7. If the length of ____

WX is 7 inches, what is ZY? Explain.

Chapter 8 ! Assignments 141

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Assignment Assignment for Lesson 8.3

Name _____________________________________________ Date ____________________ Kites and Trapezoids Properties of Kites and Trapezoids

Quadrilateral ABCD is a kite.

A

B

C

D

E

1. If m!ABC ! 95°, what is m!ADC? Explain.

2. If m!BCE ! 34°, what is m!EBC? Explain.

3. If the length of ___

AB is 16 feet, what is AD? Explain.

4. If the length of ___

BD is 25 feet, what is ED? Explain.

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