D and E are points on the sides CA and CBrespectively of a triangle ABC right angled at C.Prove that

Question

Philoid · Accepted Answer

Applying Pythagoras theorem in ΔACE, we obtain

AC² + CE² = AE² (i)

Applying Pythagoras theorem in triangle BCD, we get

BC² + CD² = BD² (ii)

Using (i) and (ii), we get

AC² + CE² + BC² + CD² = AE² + BD² (iii)

Applying Pythagoras theorem in triangle CDE, we get

DE² = CD² + CE²

Applying Pythagoras in triangle ABC, we get

AB² = AC² + CB²

Putting these values in (iii), we get

DE² + AB² = AE² + BD²