Question

For the following figure, if $\overline{WR}\perp \overline{CE}$then name all segments congruent to $\overline{WE}$.

Short answer

The segments congruent to $\overline{WE}$is $\overline{RC},\overline{CW}$ and $\overline{RE}$.

Step-by-step solution

Step 1. Check the figure.

Consider the figure $▱CREW$.

Step 2. Apply the concept of the parallelogram.

In a parallelogram, if the diagonals of a parallelogram are perpendicular then it is a rhombus.

In a rhombus, all sides are equal.

Step 3. Step description.

Here, CREW is a parallelogram.

Since $WR\perp CE$thus the parallelogram becomes a rhombus.

As all sides are equal in a rhombus thus the sides are as follows:

$\begin{array}{c}RC=CW\\ =WE\\ =RE\end{array}$

Therefore, the segments congruent to $\overline{WE}$is $\overline{CW},\overline{RC}$and $\overline{RE}$.