6 5 Trapezoid and Kites Warmup Which of

6. 5 Trapezoid and Kites

Warmup ã Which of these sums is equal to a negative number? (4) + (-7) + (6) B) (-7) + (-4) C) (-4) + (7) D) (4) + (7) ã A) A) B) C) D) In the first seven games of the basketball season, Cindy scored 8, 2, 12, 6, 8, 4 and 9 points. What was her mean number of points scored per game? 6 7 8 9

Let’s define Trapezoid A base > leg D B leg > base C <D AND <C ARE ONE PAIR OF BASE ANGLES. When the legs of a trapezoid are congruent, then the trapezoid is an isosceles trapezoid.

Isosceles Trapezoid ã If a trapezoid is isosceles, then each pair of base angles is congruent. A D B C

PQRS is an isosceles trapezoid. Find m<P, m<Q, and m<R. S 50° P R > > Q

Isosceles Trapezoid ã A trapezoid is isosceles if and only if its diagonals are congruent. A D B C

Midsegment Theorem for Trapezoid ã The midsegment of a trapezoid is parallel to each base and its length is one half the sum of the lengths of the base. B M A C N D

Examples ã The midsegment of the trapezoid is RT. Find the value of x. 7 R x 14 T x = ½ (7 + 14) x = ½ (21) x = 21/2

Examples ã The midsegment of the trapezoid is ST. Find the value of x. 8 S 11 x T 11 = ½ (8 + x) 22 = 8 + x 14 = x

Review In a rectangle ABCD, if AB = 7 x – 3, and CD = 4 x + 9, then x = ___ A) 1 B) 2 C) 3 D) 4 E) 5 7 x – 3 = 4 x + 9 -4 x 3 x – 3 = 9 +3 +3 3 x = 12 x = 4

Kite ã A kite is a quadrilateral that has two pairs of consecutive congruent sides, but opposite sides are congruent.

Theorems about Kites ã If a quadrilateral is a kite, then its diagonals are perpendicular ã If a quadrilateral is a kite, then exactly one pair of opposite angles are congruent. B A L D C

Example ã Find m<G and m<J. J Since m<G = m<J, 2(m<G) + 132° + 60° = 360° 2(m<G) + 192° = 360° 2(m<G) = 168° 60° K m<G = 84° H 132° G

Example ã Find the side length. J 12 H 12 14 12 G K