Chapter 3, Problem 13CR

To determine

To Prove: $\Delta ACF$ is isosceles.

Explanation of Solution

Given information: $\overline{CE}\cong \overline{DF}$ , $\overline{BD}\cong \overline{GE}$ , $\overline{BD}\perp \overline{CF}$ and $\overline{GE}\perp \overline{CF}$ is provided in the question which will help to find the solution.

Proof: Here, $\overline{CE}\cong \overline{DF}$ (given)

And, $CD+DE=DE+EF$

So, $CD=EF$

And, $\angle ACF=\angle AFC$ (angle opposite to equal sides are equal)

So, AC = AF (sides opposite to equal angles are equal)

Hence, we can say that

  $\Delta ACF$ is isosceles.