6.5: TRAPEZOIDS AND KITESOBJECTIVE:

TO VERIFY AND USE PROPERTIES OF

TRAPEZOIDS AND KITES

TRAPEZOID

LEGLEG

BASE ANGLES

BASE ANGLES

•The 2 parallel sides are the bases•The 2 non-parallel sides are the legs

A

B

C

D

Name the following:Bases:Legs:2 Pairs of Base Angles:

BD & ACAB & DC<A & <C<B & <D

THEOREM:

THE BASE ANGLES OF AN ISOSCELES TRAPEZOID ARE CONGRUENT.

A

B

C

D

DB

CA

.20

3

xFind

xCm

xAm

3x = x +

202x = 20X = 10

THEOREM:

THE DIAGONALS OF AN ISOSCELES TRAPEZOID ARE CONGRUENT.

EXAMPLE:If BD= 2x+10 and AC=x+15, find x and the length of the diagonals.

2x + 10 = x + 15X = 5 Therefore, the lengths of the diagonals are 20.

2 ANGLES THAT SHARE A LEG ARE SUPPLEMENTARY BECAUSE THEY ARE SAME-SIDE INTERIOR ANGLES.

180 CmAm

If the measure of angle A= 110, find the measures of the other 3 angles. < C = 70, < D = 70, & < B = 110

THEOREM:

THE DIAGONALS OF A KITE ARE PERPENDICULAR.

A kite has exactly one pair of opposite, congruent angles.

FIND THE MEASURE OF THE MISSING ANGLES.

44° 112°

1

2

What is the sum of the angles in a quadrilateral?

360 112 + 44= 156360-156= 204204/2 = 102