Theorems Dealing with Trapezoids Topic Index | Geometry Index | Regents Exam Prep Center

 Definition:   A trapezoid is a quadrilateral with exactly one pair of parallel sides.

 *Trapezoid I have only one set of parallel sides.  [The median of a trapezoid is parallel to the bases and equal to one-half the sum of the bases.]

A trapezoid has ONLY ONE set of parallel sides.
When proving a figure is a trapezoid, it is necessary to prove
that two sides are parallel and two sides are NOT parallel.

 ; The median (also called the mid-segment) of a trapezoid is a segment that connects the midpoint of one leg to the midpoint of the other leg.  Theorem:  The median (or mid-segment) of a trapezoid is parallel to each base and its length is one half the sum of the lengths of the bases. (True for ALL trapezoids.)

 Definition:  An isosceles trapezoid is a trapezoid with congruent legs.

 *Isosceles Trapezoid I have: - only one set of parallel sides - base angles congruent - legs congruent - diagonals congruent - opposite angles supplementary

 Theorems: 1. A trapezoid is isosceles if and only if the base angles are congruent. 2. A trapezoid is isosceles if and only if the diagonals are congruent. 3.  If a trapezoid is isosceles, the opposite angles are supplementary. Never assume that a trapezoid is isosceles unless you are given (or can prove) that information.

 Topic Index | Geometry Index | Regents Exam Prep Center Created by Donna Roberts