Review of Quadrilaterals

An isosceles trapezoid is a trapezoid with the non-parallel sides congruent. An additional property of isosceles trapezoids is base angles are congruent.

 

The Properties of an Isosceles Trapezoid:

1. One pair of opposite sides are parallel, i.e., \(\begin{align*}AB \parallel CD\end{align*}\).

2. Two pairs of adjacent angles are supplementary, i.e., \(\begin{align*}\angle{ABC} + \angle{BCD} = 180^\circ\end{align*}\)and \(\begin{align*}\angle{CDA} + \angle{DAB} = 180^\circ\end{align*}\).

3. Base angles are congruent, i.e., \(\begin{align*}\angle{ABC} = \angle{DAB}\end{align*}\) and \(\begin{align*}\angle{BCD} = \angle{CDA}\end{align*}\).

4. The diagonals are congruent, i.e., \(\begin{align*}AC = BD\end{align*}\).