Objectives

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.
Isos.? trap. ?s base ?
Def. of ? segs.
KM JL
Segment Add Postulate
JL JN NL
Substitute.
KM JN NL
Substitute and simplify.
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