Chapter 3.3, Problem 17PSB

To determine

To prove : The congruency of $\overline{AB}$ with respect to $\overline{CD}$ .

Explanation of Solution

Given information : In this question, we have given that $\angle ABE\cong \angle DCE$ , $\overline{BE}\cong \overline{CE}$ and $\angle ABE\cong \angle DCE$ .

Formula used: ASA Congruency rule.

Proof: As, it is given that $\angle ABE\cong \angle DCE$ , Subtracting $\angle BEC$ from both the sides, we get

  $\therefore \Delta ABE\cong \Delta DCE$

  $\Rightarrow \angle AEB\cong \angle DEC$

Now, In $\Delta ABEand\Delta DCE$

  $\angle AEB\cong \angle DEC$ (Proved above)

  $\overline{BE}\cong \overline{CE}$ (Given)

  $\angle ABE\cong \angle DCE$ (Given)

  $\therefore \Delta ABE\cong \Delta DCE$ (BY ASA Congruency rule)

  $\Rightarrow \overline{AB}\cong \overline{CD}$ (BY CPCT)