1. 6.5 Trapezoids

2. Vocabulary
A trapezoid is a quadrilateral with exactly one pair of parallel sides
base
leg
leg
base angles
base

3. The parallel sides are the bases.
The non parallel sides are the legs.
If the legs of a trapezoid are congruent, then the trapezoid is an isosceles trapezoid.

4. Theorem 6.12
If a trapezoid is isosceles, then each pair of base angles are congruent. A B
<A  <B and
<C  D D C

5. Theorem 6.13
If a trapezoid has a pair of congruent base angles, then it is isosceles. B A
If <C  <D, then
the trapezoid is
isosceles. C D

6. Midsegment of a trapezoid
The midsegment of a trapezoid is the segment that connects the midpoints of its legs. B A M N C D
The length of the midsegment of a trapezoid is
half the sum of the lengths of the bases.
MN = ½ (AB + CD)