GeometrySection 8.5

Use Properties of Trapezoids and Kites

Trapezoid

Quadrilateral with exactly one pair of parallel sides (bases)

If the legs of a trapezoid are congruent, then it is an isosceles trapezoid

leg leg

base

base

Base angles

Isosceles Trapezoid Theorems

If a trapezoid is isosceles, then each pair of base angles is congruent

If a trapezoid has a pair of congruent base angles, then it is and isosceles trapezoid.

A trapezoid is isosceles iff its diagonals are congruent.

Midsegment of a trapezoid

The segment that connects the midpoints of its legs

Midsegment Theorem for Trapezoids

The midsegment of a trapezoid is parallel to each base and its length is one half the sum of the lengths of the bases

Kite

A quadrilateral that has two pairs of consecutive congruent sides, but opposite sides are not congruent

Kite Diagonal Theorem

If a quadrilateral is a kite, then its diagonals are perpendicular

Theorem

If a quadrilateral is a kite, then exactly one pair of opposite angles are congruent

Examples

Classzone

Assignment

Section 8.5

Page 546

Problems #4 – 26 even, 34, 36