1. Trapezoids & Kites Sec 6.5 GOALS: To use properties of trapezoids and kites

2. Definition of a Trapezoid A trapezoid is a quadrilateral with exactly one pair of parallel sides. base leg

3. Defn. of an Isosceles Trapezoid An isosceles trapezoid is a trapezoid with congruent legs. base leg

4. Theorem 6.14 If a trapezoid is isosceles, then each pair of base angles is congruent.

5. Theorem 6.15 If a trapezoid has a pair of congruent base angles, then it is an isosceles trapezoid.

6. Theorem 6.16 A trapezoid is isosceles if and only if its diagonals are congruent.

7. Example ABCD is an isosceles trapezoid. Find the measure of the angles not shown.

8. Example Show that PQRS is a trapezoid. B (0, 5) C (4, 7) A (5, 0) D (7, 4)

9. Midsegment of a Trapezoid The midsegment of a trapezoid is the segment that connects the midpoints of its legs. Theorem 6.17 The midsegment of a trapezoid is parallel to each base and its length is one-half of the sum of the lengths of the bases.

10. Example Find the length of the midsegment, MN.

11. Kite A kite is a quadrilateral that has two pairs of consecutive congruent sides, but opposite sides are not congruent.

12. Kite Theorem 6.18 If a quadrilateral is a kite, then its diagonals are perpendicular.

13. Kite Theorem 6.19 If a quadrilateral is a kite, then exactly one pair of opposite angles are congruent.

14. Example Find AD and AB.

15. Example ABCD is a kite. Find the measure of angles B, C, and D.

16. Homework Page - See assignment guide