Chapter 4.7, Problem 1ST3

To determine

To prove: that $\Delta AFE\cong \Delta BFD$ . To find corresponding parts from this second pair of congruent triangle and to prove the first pair of triangles congruent.

Explanation of Solution

Given information:

Already proved $\Delta ABE\cong \Delta BAD$ .

  

Calculation:

If $\Delta ABE\cong \Delta BAD$ ,

Then from $\Delta ABE$ and $\Delta BAD$ by congruent part od the congruent triangles,

  $\begin{array}{c}\angle AEB\cong \angle ADB\\ \overline{AE}\cong \overline{BD}\\ \angle BAE\cong \angle ABD\\ \angle ABE\cong \angle BAD\end{array}$

Therefore, in $\Delta AFE$ and $\Delta BFD$ , $\angle FAE\cong \angle FBD$

BY angle side angle postulate,

  $\Delta AFE\cong \Delta BFD$