Chapter 4, Problem 3RP

To determine

To Prove: $BD\perp AC.$

Explanation of Solution

Given information: $\angle ADB=\angle CDB$

Formula Used: Linear pair axiom.

Proof:

  $\begin{array}{l}\angle ADB=\angle CDB \left(\text{Given}\right)\\ \angle ADB+\angle CDB={180}^{\circ }\left(\text{Linear pair axiom}\right)\\ \therefore \angle ADB+\angle ADB={180}^{\circ }\\ \therefore 2\angle ADB={180}^{\circ }\\ \therefore \angle ADB={90}^{\circ }\\ \therefore BD\perp AC.\end{array}$