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## Question:

13.) Write a Paragraph proof ( Thanks!!)

Given Line BC = Line EC and Line AC = DC Line

Prove Line BA= Line ED

## Answer:

The **paragraph proof** has been explained below to **prove that Line BA = Line ED.**

We are given;

BC = EC

AC = DC

This means that C is the midpoint of BE and AD.

Thus, according to **vertically opposite angles theorem**, we can say that;

**m∠DCE = m∠ACB**

This means we now have **2 corresponding sides that are equal **and the **included corresponding equal angle.**

Therefore, we can deduce that ΔABC ≅ ΔDEC with **SAS (Side-Angle-Side) congruency theorem.**

Now, since** ΔABC ≅ ΔDEC**, we can say from **(CPCTC) **that AB = DE due to the fact that corresponding parts of congruent triangles are also congruent.

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