#### Transcript of Properties of Kites and Trapezoids

Theorems:

theorem 6.14 theorem 6.15 theorem 6.16

if a trapezoid is isosceles, then

each pair of base angles is congruent.

*<A <B, <C <D

A B

D C

**Vocabulary:**

*trapezoid

*bases

*base angles

*legs

*isosceles trapezoid

*midsegment

*kite

**by: Victoria, Michelle, Alyssa, & Savanna**

**Properties of Kites and Trapezoids**

if a trapezoid has a pair of congruent

base angles, then it is an isosceles

trapezoid.

*ABCD is an isosceles trapezoid.

A B

D C

a trapezoid is isosceles if and

only if its diagonals are congruent.

*ABCD is an isosceles trapezoid if and

only if its diagonals are congruent.

*ABCD is isosceles if and only if AC

BD.

A B

D C

**Example 1:**

PQRS is an isosceles trapezoid . Find m<P, m<Q, and m<R.

S R

50

P Q

PQRS is an isosceles trapezoid, so m<R=m<S= 50 degrees. <S and <P are consecutive interior angles formed by the parallel lines, they are supplementary. So, m<P=130 degrees, m<Q=m<Q=130 degrees.

Trapezoid :

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

*The parallel sides of a trapezoids are bases.

*The legs are the nonparallel sides of a trapezoid.

Isosceles Trapezoid :

* An isosceles trapezoid is a trapezoid with congruent legs.

Midsegment:

*the midsegment of a trpezoid is the segment that connects the midpoints of its legs.

*theorem 6.17 is similar to the Midsegment Theorem for triangles.

A B

midsegment

D C

Theorem 6.17

*the midsegment of a trapezoid is the parallel to each base and its length is one half the sum of the lengths of the bases.

MN AD, MN BC, MN=1/2(AD+BC)

A B

E F

D C

**Theorems about kites:**

*Theorem 6.18: if a quadrilateral is a kite,

the its diagonals are perpendicular.

-AC

BD

*Theorem 6.19: if a quadrilateral is a kite,

then exactly one pair of oppisite angles are

congruent.

-<A <C,<B

<D

Example 2:

Find m<A and m<C in the diagram.

132

60

GHJK is a kite, so <G = <J and m<G=m<J

2(m<G)+132 +60 =360

-sum of measures of int.<s of a quad. is 360

2(m<G)=168

-simplify

2 2

m<G=84

-divided each side by 2

*so, m<J= m<G=84

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