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Q3

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Found in: Page 169

### Geometry

Book edition Student Edition
Author(s) Ray C. Jurgensen, Richard G. Brown, John W. Jurgensen
Pages 227 pages
ISBN 9780395977279

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

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

See the 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 $\overline{RE}$.