Question

D and E are the point on the side CA and CB respectively. of a triangle ABC right angled at C. Prove that
AE? + BD2 = AB? + DE?

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Answer 1

Given below... plz mark it as brainliest

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,

BD 2 =DC2 +BC2 .....(2)

In △ABC,

AB2 =AC2 +BC2 .....(3)

In △DCE,

DE2 =DC2 +CE2 .....(4)

Now,

AE2 +BD2 =AB2 +DE2

AC2 +CE2 +DC2 +BC2 =AC2 +BC2 +DC2 +CE2

L.H.S. = R.H.S.

Hence proved.