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

Trapezoid General Definition one set of parallel sides

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

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

Examples Trap

Kite Two pairs of consecutive sides congruent

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

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

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

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

Examples Kites

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

Homework Pg 271 1-8 Honors 9 and 10