Chapter 8.3, Problem 4PSA

To determine

To prove : The similarity of $\Delta BCD$ with respect to $\Delta FED$ .

Explanation of Solution

Given information : Here, we have given that $\overline{AC}\cong \overline{AE}$ and $\angle CBD\cong \angle EFD$

Proof: As, $\overline{AC}\cong \overline{AE}$ ,

  $\Rightarrow \angle ACE\cong \angle AEC$ (Angles opposite to equal sides are equal)

Or, $\angle BCD\cong \angle FED$

Now, In $\Delta BCD$ and $\Delta FED$

  $\angle BCD\cong \angle FED$ (Proved above)

  $\angle CBD\cong EFD$ (Given)

  $\Rightarrow \Delta BCD\sim \Delta FED$ (By AA Similarity Rule)