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
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.