Chapter 4, Problem 16RP

To determine

To Verify: $\angle 1=\angle 2$

Explanation of Solution

Given information: AD is perpendicular bisector of BC

Formula Used: congruency of triangles and properties of angles.

Verification:

  $\begin{array}{l}\therefore BD=DC\text{And}\angle ADB=\angle ADC={90}^{\circ }\\ AD=AD(common)\\ \therefore \Delta ACD\cong \Delta ABD(SAS)\\ \therefore \angle DAC=\angle DAB(CPCT)\\ \angle BFD=\angle CFD(CPCT)\\ \angle FAB+\angle 2=\angle FAC+\angle 1\left(\text{Exterior angle property}\right)\\ \therefore \angle 2=\angle 1(\text{As}\angle FAC=\angle FAB)\end{array}$