Chapter 7, Problem 25RP

To determine

To prove $△ABF$ isosceles.

Explanation of Solution

Given:

  $\begin{array}{l}\overline{BC}\cong \overline{FE}\\ \angle C\cong \angle E\end{array}$

  

Calculation:-

In triangle Angle C is Congruent to Angle E

Given-

  $\angle BDC\cong \angle FDE$

If two angles are vertical angles, then they are congruent.

  $△CBD\cong △EFD$ By AAS congruency.

  $\angle BDC\cong \angle FDE(ByCPCTC)$

  $\angle DBD\cong \angle DFF$

  $\angle ABF\cong \angle \text{ A}FB$

If congruent angles are subtracted from straight angles, then the differences are congruent

Triangle ABF is isosceles.

If 2 angles in triangle are congruent, then it is an isosceles triangle