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

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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

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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.

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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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