Question

For the following figure, if $OE=4$and $WE=8$, name two segments congruent to $\overline{WE}$.

Short answer

The two segments are congruent to $\overline{WE}$ is $\overline{CR},\overline{CE}$ .

Step-by-step solution

Step 1. Check the figure.

Consider the figure $▱CREW$.

Step 2. Apply the concept of the parallelogram.

In a parallelogram, opposite sides of a parallelogram are equal to each other, and diagonals of a parallelogram bisect each other.

Step 3. Step description.

Here, CREW is a parallelogram.

Since the opposite sides are congruent in a parallelogram, thus $\overline{CR}$and $\overline{WE}$are the opposite sides and $\overline{WE}\cong \overline{CR}$.

As the diagonal bisects each other thus $\overline{CE}$and $\overline{WR}$bisect each other.

Step 4. Step description.

From the figure, O is the midpoint of $\overline{CE}$such that $CE=OE=4$.

Thus, simplify the equation as follows:

$\begin{array}{l}CE-CO+OE\\ CE=4+4\\ CE=8\end{array}$

Since $WE=CE$this $\overline{WE}\cong \overline{CE}$

Therefore, the segments are congruent to $\overline{WE}$are $\overline{CE},\overline{CR}$.