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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 base1 leg leg base2 Types of Trapezoids Scalene or basic trap – previous page Right Trap – has two right angles on same leg base1 leg leg base2 Isosceles Trap – both legs are congruent base1 leg leg base2 Diagonals of an Isosceles Trapezoid Can you prove the diagonals congruent Given: Isosceles Trapezoid Prove: AC=BD B A C D Examples Trap Kite Two pairs of consecutive sides congruent Kite Properties Given: Kite Prove: <A=<C B C A Angles formed by non congruent sides are congruent D Kite Properties Given: Kite Prove: <ADB=<CDB and <ABD=<CBD (segment BD is an angle bisector) Diagonal connecting non congruent angles bisects Those angles B C A D Kite Properties Given: Kite Prove: AE=CE Diagonal connecting the congruent angles is bisected by the other diagonal B A C E D 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