Question

if in a right angle triangle ABC, right angled at A, AD perpendicular to BC , then prove that AB²+CD²=BD²+AC²​

Answer 1

Since triangles ABD and ACD are right-angled triangles at D.

   ∴ AD2=AD2+BD2..(i)

and,   AC2=AD2+CD2.(ii)

Subtracting (ii) from (i), we get

      AB2−AC2=BD2−CD2

⇒ AB2+CD2=AC2+BD2      [Hence proved]

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