1. Trapezoids and Kites
Objective: Students will be able to apply additional properties to prove shapes are triangles and kites.

2. Trapezoid
General Definition one set of parallel sides

3. Types of Trapezoids
Scalene or basic trap – previous page Right Trap – has two right angles on same leg Isosceles Trap – both legs are congruent

4. Diagonals of an Isosceles Trapezoid
Can you prove the diagonals congruent Given: Isosceles Trapezoid Prove: AC=BD

5. Examples Trap

6. Kite
Two pairs of consecutive sides congruent

7. Kite Properties Given: Kite Prove: <A=<C
Angles formed by non congruent sides are congruent

8. Kite Properties
Given: Kite Prove: <ADB=<CDB and <ABD=<CBD (segment BD is an angle bisector)
Diagonal connecting non congruent angles bisects
Those angles

9. Kite Properties Given: Kite Prove: AE=CE
Diagonal connecting the congruent angles is bisected by the other diagonal

10. Kite Properties
The two diagonals of a kite are perpendicular How would you prove this? Pythagorean Theroem

11. Examples Kites

12. Summary
Trapezoid – 1 pair of parallel sides Right Trapezoid – 1 pair of parallel sides, with 1 leg perpendicular to both sides Isosceles Trapezoid – 1 pair of parallel sides and both legs are congruent - diagonals are congruent Kite – 2 pairs of consecutive sides congruent - angles formed by non congruent sides are congruent - diagonals are perpendicular - diagonal connecting non congruent angles is an angle bisector - diagonal connecting congruent angles is bisected by other diagonal

13. Homework
Pg Honors 9 and 10