1

Objectives

• State the properties of trapezoids and kites

• Solve problems involving kites and trapezoids

2

Trapezoid Definitions

• The parallel sides of a trapezoid are the bases

• The non-parallel sides of a trapezoid are the legs

• The angles that share a base are the base angles.

3

Theorem 6-15 Base Angles of Isosceles Trapezoid

• The base angles of an isosceles trapezoid are congruent.

4

Example: Base angles of isosceles trapezoid

Same side interior angles are suppl.

Substitution

Subtraction

The base angles of an isosceles trapezoid are congruent.

5

Theorem 6-16

• A trapezoid is isosceles if and only if its diagonals are congruent

6

Example: Diagonals of Isosceles Trapezoid

JN = 10.6, and NL = 14.8. Find KM.

Def. of segs.

Segment Add Postulate

Substitute.

Substitute and simplify.

Isos. trap. s base

KM = JL

JL = JN + NL

KM = JN + NL

KM = 10.6 + 14.8 = 25.4

7

Theorem 6-17 Diagonals of a Kite

• The diagonals of a kite are perpendicular

8

Example: Diagonals of a Kite

Diagonals of a kite are perpendicular

∠2 is the complement of ∠DBC

BD ≅ BD Reflexive Prop. of Congruence