Chapter 5.1, Problem 1WE

To determine

To identify: two segments that are congruent to $\overline{WE}$ .

Answer to Problem 1WE

$\overline{CR}$ And $\overline{CE}$

Explanation of Solution

Given:

The diagram:

  $OE=4$

  $WE=8$

Concept Used:

Theorem 5-1: opposite sides of parallelogram are equal to each other

Theorem 5-3: Parallelogram’s diagonal bisects each other.

Consider the figure shown below:

Here it is given that $CREW$ is a parallelogram.

So, by theorem 5-1, its opposite sides are congruent.

Here, $\overline{CR}$ and $\overline{WE}$ are the opposite sides of the parallelogram $CREW$ . So,

  $\overline{WE}\cong \overline{CR}$

Now, by theorem 5-3, $\overline{CE}$ and $\overline{WR}$ bisect each other.

That is, O is the midpoint of $\overline{CE}$ .

  $CO=OE=4$

Thus,

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

Therefore,

  $WE=8=CE$

Hence,

  $\overline{WE}\cong \overline{CE}$