Question

triangle ABC is a right angled triangle at C . D is a point on the side AC and E is a point on the side BC show that AB² + DE² = AE²+ BD²​

Answer 1

Step-by-step explanation:

Given:- △ABC, right angled at C.

Two points D and E are on the sides AC and AB.

To prove:- AE²+BD²=AB²+DE²

Construction:- Join the point D with B and E and point E with A.

Proof:-

Using pythagoras theorem,

Hypotenuse²=Perpendicular²+Base²

In △ACE,

AE²=AC²+CE² .....(1)

In △BCD,

BD²=DC²+BC² .....(2)

In △ABC,

AB²=AC²+BC² .....(3)

In △DCE,

DE²=DC²+CE² .....(4)

Now from equations (1),(2),(3) and (4),

AE²+BD²=AB²+DE²

Therefore, Proved.