Chapter 4, Problem 15RP

To determine

To Verify: $AD\perp CE.$

Explanation of Solution

Given information: $AB=AF,BD=DF,\angle 1=\angle 2.$

Formula Used: Congruency of triangle and properties of angles.

Verification:

  $\begin{array}{l}AF=AB,FD=BD(given)\\ AD=AD(common)\\ \therefore \Delta AFD\cong \Delta ABD(sss)\\ \angle ADF=\angle ADB(CPCT)\\ \angle 1=\angle 2(given)\\ \therefore \angle 1+\angle ADB=\angle 2+\angle ADF\\ \therefore \angle ADE=\angle ADC.\\ \text{By linear pair axiom,}\\ \angle ADE+\angle ADC={180}^{\circ }\\ \therefore \angle ADE=\angle ADC={90}^{\circ }\end{array}$