Question

complete the proof to show that abcd is a parallelogram. b(-3,4) c(2,2) a(-2,-2) d(3,-4)
the slope of bc is $\frac{4 - 2}{-3 - 2}=-\frac{2}{5}$
the slope of ad is $\frac{-4-(-2)}{3-(-2)}=\frac{-4 + 2}{3+2}=-\frac{2}{5}$
the slope of cd is $\frac{2-(-4)}{2 - 3}=\frac{2 + 4}{2-3}=\frac{6}{-1}=-6$
$overline{bc}paralleloverline{ad}$ and $overline{cd}paralleloverline{ba}$ because the
. therefore, abcd is a
parallelogram because both pairs of opposite sides are parallel.
lengths of consecutive sides are not equal
slopes of consecutive sides are not equal
slopes of opposite sides are equal
lengths of opposite sides are equal

Explanation:

Step1: Recall parallel - line condition

In a coordinate - plane, two lines are parallel if and only if their slopes are equal.

Step2: Analyze the property for a parallelogram

A quadrilateral is a parallelogram if both pairs of opposite sides are parallel. This means the slopes of opposite sides must be equal.

Answer:

slopes of opposite sides are equal