Question

D and E are the points on the sides CA and CB of ABC , right angle at C. Prove that AE2+BD2=AB2+DE2​

Answer 1

Answer:

Step-by-step explanation:

To prove: AE2 +BD2 = AB2 +DE2

Proof:

In triangle ACB , <C=90°

AB2 = AC2 + CB2 ••••••(1)

In triangle DCE <C =90°

DE2 = DC2 + CE2 •••••••(2)

Now, in triangle ACE , <C =90°

AE2 = AC2 + CE2 ••••••••(3)

IN triangle BCD <C =90°

BD2= DC2 + CB2 ••••••••(4)

ADDING (3) AND (4)

AE2 + BD2 = AC2+ CE2 +CD2 +CB2

= (AC2+ CB2 ) +(CE2 +CD2)

=(AB2 ) +(DE2)

AE2 +BD2 =AB2 +DE2

HENCE PROVED!!!

Answer 2

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