6-6:Trapezoids and Kites

CP GeometryMr. Gallo

A B

CD

A B

CD

What is a Trapezoid

Trapezoid

Isosceles Trapezoid

leg

leg

Base

Base Angles

legleg Base Angles

If a quadrilateral is a trapezoid, ________________________________________.one pair of parallel sides

then it has exactly

Base

Base

BaseThe legs in an

isosceles trapezoid are congruent.

Theorem 6-19If a quadrilateral is an isosceles trapezoid, _______________________________________.then each pair of base angles is congruent A B

CD

____A BThen the following angles are congruent:

____D C

b. Yes; so SSI angles are supplementary.

Complete Got It? #1 p. 390a.

What are the values of x and y in the isosceles triangle below if is a midsegment?

32

y

x

E

D

C

A

B

180 3274

2m B y

180 74 106m BDE x

Theorem 6-20If a quadrilateral is an isosceles trapezoid, ______________________________.then its diagonals are congruent

A B

CD

So, ____ _____

The diagonals of isosceles trapezoid ABCD are:

____ & ____AC BD

AC BD

Theorem 6-21If a quadrilateral is a trapezoid then:

1). _____________________________________

2). __________________________________________________________________________the length of the midsegment is half

the midsegment is parallel to the bases

the sum of the lengths of the bases

FE

A B

CD

1

2EF AB DC

is the midsegment of trapezoid WXYZ. What is x? 6x-12

2x+10

18

UT

X Y

ZW

1

2TU XY WZ

12 10 6 12 18

2x x

2 2 10 6 6x x

4 20 6 6x x

14 2x

7 x

What is a Kite

D B

C

A

If a quadrilateral is a kite, _________________________________________________________________________________.

consecutive sides congruent and no opposite

then it has two pairs of

sides congruentD B

C

A

Another example of

a kite

Theorem 6-20If a quadrilateral is a kite,__________________________________.then its diagonals are perpendicular

So, ____ _____The diagonals of kite ABCD are: ____ & ____ AC BD

AC BD

D B

C

A

Properties of Kites

MS A

T

R

In kite STAR, ST=_____

SR=_____

SM=_____

_____

_______

_______

_______

SA

TSR

STM

TRS

TARAMA

TRTAR

TMATRA

Homework: p.394 #7-23 odd, 28-36 even