Module 6.6 Trapezoids and kites

Trapezoid

A quadrilateral with exactly one pair of parallel sides

Bases of a trapezoid

The parallel sides of a trapezoid

Legs of a trapezoid

The nonparallel sides of a trapezoid

Base angles

Angles formed by the base and one of the legs

Isosceles trapezoid

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

Theorem 6.21 Isosceles Trapezoids

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

Theorem 6.22 Isosceles Trapezoids

If a trapezoid has one pair of congruent base angles, then it is an isosceles trapezoid

Theorem 6.23

A trapezoid is isosceles if and only if it’s diagonals are congruent

Midsegment of a trapezoid

The segment that connects the midpoints of the legs of the trapezoid

Trapezoid midsegment theorem

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

Kite

A quadrilateral with exactly two pair of consecutive congruent sides

Kite theorem 6.25

If a quadrilateral is a kite then it’s diagonals are perpendicular

Kite theorem 6.26

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