6.5: TRAPEZOIDS AND KITES OBJECTIVE: TO VERIFY AND USE PROPERTIES OF TRAPEZOIDS AND KITES

TRAPEZOID LEG 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 & AC AB & DC <A & <C <B & <D

THEOREM: THE BASE ANGLES OF AN ISOSCELES TRAPEZOID ARE CONGRUENT. A B C D 3x = x x = 20 X = 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 + 15 X = 5 Therefore, the lengths of the diagonals are 20.

2 ANGLES THAT SHARE A LEG ARE SUPPLEMENTARY BECAUSE THEY ARE SAME-SIDE INTERIOR ANGLES. 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? = = /2 = 102