Question

In a triangle ABC, AD is perpendicular to BC. Prove that AB²-BD²=AC²-CD²

Answer 1

In triangle ABC, AD is perpendicular to BC

therefore, in triangle ABD and triangle ACD

by pythagoras theorem

AD² = AB² + BD² ......1.. ( in triangle ABD)

AD² = AC² + CD² ......2...( in triangle ACD)

therefore from 1and 2

AB² ‐ BD² = AC² ‐ CD²