Question

complete the proof to show that abcd is a parallelogram. bc || ad and cd || ba because the _____________. therefore, abcd is a parallelogram because both pairs of opposite sides are parallel. lengths of consecutive sides are not equal slopes of opposite sides are equal lengths of opposite sides are equal slopes of consecutive sides are not equal the slope of bc is $\frac{4 - 2}{-3 - 2}=-\frac{2}{5}$ the slope of ad is $\frac{-4-(-2)}{3-(-2)}=\frac{-4 + 2}{3 + 2}=-\frac{2}{5}$

Explanation:

Step1: Recall parallelogram property

Parallel lines have equal slopes. In a parallelogram, opposite - sides are parallel.

Step2: Analyze given slopes

The slopes of $\overline{BC}$ and $\overline{AD}$ are calculated and found to be equal. This shows one pair of opposite sides is parallel. Similarly, if we calculate the slopes of the other pair of opposite sides, we will find them to be equal too. Since parallel lines have equal slopes, a quadrilateral with both pairs of opposite - sides having equal slopes (i.e., opposite sides are parallel) is a parallelogram.

Answer:

slopes of opposite sides are equal