Theorems Dealing with Trapezoids
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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.