Chapter 4, Problem 4RP

To determine

To Prove: $CF\perp AE.$

Explanation of Solution

Given information: $\angle 1=\angle 4,$ FC bisects $\angle BFD.$ .

Formula Used: Linear pair axiom.

Proof:

  $\begin{array}{l}\angle 1=\angle 4\left(\text{Given}\right)\\ \angle 2=\angle 3\text{(Giving FC bisect)}\\ \therefore \angle 1+\angle 2=\angle 3+\angle 4\\ \therefore \angle AFC=\angle EFC\\ \text{By linear pair axiom,}\\ \angle AFC=\angle EFC={180}^{\circ }\\ \therefore \angle AFV={90}^{\circ }=\angle EFC.\end{array}$