1. Kites & Trapezoids To recognize and apply the properties of trapezoids

2. Definitions Trapezoid - Quadrilateral with exactly one pair of parallel sides Bases - the parallel sides in a trapezoid Legs - the non parallel sides Base angles - angles formed with the base and legs Isosceles trapezoid - trapezoid w/ congruent legs

3. Theorems Isosceles Trapezoid Both pairs of base angles of an isosceles trapezoid are congruent The diagonals of an isosceles trapezoid are congruent

4. Definition Median - segment that joins the midpt of the legs of a trapezoid AKA-midsegment Theorem The median is ll to the bases and its measure is 1/2 the sum of the measures of the bases

5. Example G H K L J I Given trap. GHIJ w/ median KL, find x 3x - 1 10 7x + 1 KL = 1/2(GH + JI) 10 = 1/2 (3x - 1 + 7x + 1) 10 = 1/2 (10x) 10 = 5x 2 = x

6. Example E 4x - 10 Z 13 B A 3x + 8 O I Find x given trap EZOI and median AB. 13 = 1/2(3x + 8 + 4x - 10) 13 = 1/2(7x - 2) 26 = 7x - 2 28 = 7x 4 = x

7. A quadrilateral that has 2 pairs of consecutive congruent sides. Properties: The diagonals are perpendicular Exactly one pair of opposite angles are congruent. Kite

8. Homework • PG 546 3 – 23 odd, 24 – 27, 32