1. 6.5 Trapezoid and Kites

2. Warmup  Which of these sums is equal to a negative number? A) (4) + (-7) + (6) B) (-7) + (-4) C) (-4) + (7) D) (4) + (7)  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? A) 6 B) 7 C) 8 D) 9

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

4. Isosceles Trapezoid  If a trapezoid is isosceles, then each pair of base angles is congruent. A B CD

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

6. Isosceles Trapezoid  A trapezoid is isosceles if and only if its diagonals are congruent. A B CD

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

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

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

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

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

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

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

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