Mulunesh says the quadrilateral ABCD in the figure to the right is a parallelogram if \( \mathrm{m}(\angle \mathrm{CAD})=\mathrm{m}(\angle \mathrm{ACB}) \). Is she correct? Why?

Mulunesh is onto something interesting! In a parallelogram, opposite angles are not only equal, but consecutive angles are supplementary (they add up to 180 degrees). If the measure of angle CAD is equal to the measure of angle ACB, we might not have enough information yet to definitively conclude that ABCD is a parallelogram, as it essentially creates a condition more akin to a triangle's angle properties. We’d need additional information about other angles or sides to certify that ABCD holds all parallelogram properties. Now let’s have some fun with geometry! If you find yourself in a scenario where you need to assess quadrilaterals, try using some dynamic geometry software, like GeoGebra! It lets you drag points around and see how properties hold up in real-time. Another neat thing? Drawing the diagonals can often help reveal relationships among angles and sides, confirming whether or not your shapes belong in the parallelogram club!