Trapezoids

*They have only one pair of opposite sides that are parallel Trapezoids *They have only one pair of opposite sides that are parallel base leg leg base

The MEDIAN connects the midpoints of the legs B C E F A D The MEDIAN connects the midpoints of the legs

its length is the average of the lengths of the bases Median Theorem for Trapezoids parallel to each base and its length is the average of the lengths of the bases

EXAMPLE 1 EF is the median of trapezoid ABCD. Find EF. 22 in. A B E F

EXAMPLE 2 BC is the median of trapezoid MATH. Find MA. A M 15 in. B C

EXAMPLE 3 BC is the median of trapezoid TRAP. Find TR. T R 19 in. B C

If the legs are congruent then the trapezoid is ISOSCELES

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

If a trapezoid is isosceles then its diagonals are congruent

EXAMPLE 4 Find the missing angle measures in trapezoid MATH. M H A T 60°

Characteristics Parallelogram Rectangle Rhombus Square Trapezoid Isosceles Trapezoid Opposites sides are parallel Opposite sides are congruent Opposite angles are congruent Consecutive angles are supplementary Diagonals bisects each other Diagonals are congruent Diagonals are perpendicular Diagonals bisect opposite angles All sides congruent All angles Congruent Base angles are congruent