Question

If AD is perpendicular to BC and BD/DA = DA/DC then prove that triangle ABC is a right triangle

Answer 1

In right  ΔADB and ΔADC, we have:

AB² = AD² +BD² 

AC² = AD²+ DC²

adding up both

AB² + AC² = 2AD² + BD² + DC²

= 2BD x CD + BD² + CD²                         as AD x 2 = BD x CD

= (BD + CD)² = BC²

Thus, in ΔABC: AB² + AC² = BC²

Hence, ΔABC is a right triangle and has right angled at A.

Answer 2

Hence (AB)^2+(AC)^2=(BC)^2
BY CONVERSE OF PYTHAGORAS THM. WE GET IT IS AN RIGHT ANGLED TRIANGLE