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Properties of Kites and Trapezoids

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by

Vicky Reyes

on 10 December 2013

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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
Thank
You

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