Brian McCall

**Univ. of Wisconsin**

J.D. Univ. of Wisconsin Law school

Brian was a geometry teacher through the Teach for America program and started the geometry program at his school

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Trapezoids are one of the most common quadrilaterals. A trapezoid has one pair of parallel sides. When a trapezoid has two sets of parallel sides, it is a more specific type of trapezoid called a parallelogram. A more specific type of trapezoid is called an isosceles trapezoid. In addition to one pair of parallel sides, isosceles **trapezoid properties** include congruent legs, base angles and diagonals.

One of the common quadrilaterals is a trapezoid and what defines a trapezoid? Well the only thing we know about trapezoid is that we have 1 pair of parallel sides. If we had 2 pairs of parallel sides it wouldn't be a trapezoid. We could be even more specific and say that it is a parallelogram, so again a trapezoid just has 1 pair of parallel sides.

There's a more specific example of a trapezoid and that's an isosceles trapezoid which means you not only have 1 pair of parallel but these legs are also congruent. So the non parallel legs are congruent, which creates 2 special things. The first is that the base angles are congruent. So you have 2 pairs of base angles, these 2 angles are congruent and these 2 base angles are congruent.

Another consequence is that the diagonals are congruent. So if I drew in my diagonals here I will be able to say that they're both congruent to each other. Since these 2 angles are part of a transversal we can say that they are same side interior angles. So consecutive base angle are always going to be supplementary, so these 2 angles are supplementary and these 2 same side interior angles are also going to be supplementary. So a couple of key things about the trapezoid when you have 2 legs that are congruent in a trapezoid.