Trapezoids and Kites

Additional Properties

Trapezoid

General Definitionone set of parallel sides

leg leg

base2

base1

Types of Trapezoids

Scalene or basic trap – previous pageRight Trap – has two right angles on same leg

Isosceles Trap – both legs are congruent

leg leg

base2

base1

leg leg

base2

base1

Diagonals of an Isosceles Trapezoid

Can you prove the diagonals congruentGiven: Isosceles TrapezoidProve: AC=BD

C

A D

B

Examples Trap

Kite

Two pairs of consecutive sides congruent

Kite Properties

Given: KiteProve: <A=<C

D

C

B

A

Angles formed by non congruent sides are congruent

Kite Properties

Given: KiteProve: <ADB=<CDB and

<ABD=<CBD (segment BD isan angle bisector)

D

C

B

A

Diagonal connecting non congruent angles bisectsThose angles

Kite Properties

Given: KiteProve: AE=CE

E

D

C

B

A

Diagonal connecting the congruent angles is bisected by the other diagonal

Kite Properties

The two diagonals of a kite are perpendicularHow would you prove this?Pythagorean Theroem

Examples Kites

SummaryTrapezoid – 1 pair of parallel sidesRight Trapezoid – 1 pair of parallel sides, with 1 leg perpendicular to both sidesIsosceles Trapezoid – 1 pair of parallel sides and both legs are congruent

- diagonals are congruentKite – 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