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In this lesson you will:

� use properties of trapezoids and kites.

A ___________________ is a quadrilateral with exactly one pair of parallel sides.

The parallel sides are the ___________ and the nonparallel sides are the __________.

An __________________ trapezoid is a trapezoid with congruent legs.

Theorem about

Isosceles

Trapezoids

Description Diagram/Picture Important Characteristics

Base Angles

Theorem

Converse to Base

Angles Theorem

Diagonals Theorem

Consecutive Angles

Property .

Example 1: Set up an equation and solve for the variables.

Example 2: Find x if the perimeter is 60 in.

Example 3: Set up an equation to solve for the variables.

13 in

28 in

x

A B

x

D C

D

A B

x

C

A B

x

D C

y°

112°

z°

x°

c°

d°

120°

56°

A B

x

D C

Theorem about

Trapezoids Description Diagram/Picture Important Characteristics

Midsegment

Theorem .

Example 4: Solve for x. Example 5: Solve for each variable.

Example 6: Set up an equation to solve for the variables.

� Kite Conjecture #1: The vertex angles of a kite are by their diagonal.

� Kite Conjecture #2: The non-vertex angles of a kite are (from bilateral symmetry).

� Kite Conjecture #3: The diagonals of a kite are .

� Kite Conjecture #4: The diagonal connecting the non-vertex angles is by the

other diagonal.

Example 7: Find the value of each variable. Example 8: Find k if the perimeter is 118 inches.

Example 9: Find the value of each variable. Example 10: Find the value of each variable.

A B

D C

M N

68º 56º

wº

vº

45 in

33 in

y

x

15cm

26cm