1. 6.5 Trapezoids and Kites Homework: the last 4 slides 1 of 21

2. Chapter 6 – Quadrilaterals 6.5 - Trapezoids and kites A trapezoid is a quadrilateral with exactly one pair of parallel sides. The parallel sides are called the bases. The nonparallel sides are called legs. An isosceles trapezoid has two congruent legs. base leg Isosceles Trapezoid 2 of 21

3. Chapter 6 – Quadrilaterals 6.5 - Trapezoids and kites Theorem 6.14 If a trapezoid is isosceles, then each pair of base angles is congruent.  A  B,  C  D A B C D Theorem 6.15 If a trapezoid has a pair of congruent base angles then it is an isosceles trapezoid. A B C D 3 of 21

4. Chapter 6 – Quadrilaterals 6.5 - Trapezoids and kites Theorem 6.16 If a trapezoid is isosceles if and only if its diagonals are congruent. A B C D 4 of 21

5. Chapter 6 – Quadrilaterals 6.5 - Trapezoids and kites A midsegment of a trapezoid is the segment that connects the midpoints of its legs. Theorem 6.17 Midsegment theorem of Trapezoids The midsegment of a trapezoid is parallel to each base and its length is one-half the sum of the lengths of the bases. MN || AD, MN || BC, MN = (AD + BC) 1212 A B CC D N M Midsegment 5 of 21

6. Chapter 6 – Quadrilaterals 6.5 - Trapezoids and kites A kite is a quadrilateral that has two pairs of consecutive congruent sides, but opposite sides are not congruent. 6 of 21

7. Chapter 6 – Quadrilaterals 6.5 - Trapezoids and kites Theorem 6.18 If a quadrilateral is a kite, then its diagonals are perpendicular. B A C D AC  BD Theorem 6.19 If a quadrilateral is a kite, then exactly one pair of opposite angles are congruent. B A C D  A   C,  B   D 7 of 21

8. Chapter 6 – Quadrilaterals 6.5 - Trapezoids and kites A. WXYZ is a Kite. Find the side length. W Z X Y 12 20 12 WX = 8 of 21

9. Chapter 6 – Quadrilaterals 6.5 - Trapezoids and kites B.Find m  G and m  J of this kite. 132° 60° G H J K 9 of 21

10. Chapter 6 – Quadrilaterals 6.5 - Trapezoids and kites C. PQRS is an isosceles trapezoid. Find m  P, m  Q and m  R. S P Q R 50° 10 of 21

11. Chapter 6 – Quadrilaterals 6.5 - Trapezoids and kites D. A baker is making a 3-layer cake. The top layer has a diameter of 8 inches and the bottom layer has a diameter of 20 inches. How big should the middle layer be? 11 of 21