Question

For the following figure, if $RE=EW$then name all angles congruent to $\angle ERW$.

Short answer

The angles are congruent to $\angle ERW$is $\angle CRW,\angle EWR$.

Step-by-step solution

Step 1. Check the figure.

Consider the figure $▱CREW$.

Step 2. Apply the concept of a 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 then the equations are as follows:

$\begin{array}{l}CW=RE\\ RE=WE\end{array}$

Conclude from the above equation as follows:

$CW=WE$

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

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

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

This triangle is an Isosceles triangle and in the Isosceles triangle, the base angle is equal then $\angle ERW=\angle EWR$.

Step 4. Step description.

From the figure, WE and RW is transversal thus alternate angles are equal such that $\angle CRW=\angle EWR$.

Therefore, the angles congruent to $\angle ERW$are $\angle CRW,\angle EWR$.