Question

In a triangle ABC, AD is perpendicular to BC. Prove that AB^2 + CD^2 = AC^2 + BD^2.​

Answer 1

Step-by-step explanation:

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

∴ AD ²=AD² +BD².....(i)

and, AC²=AD²+CD²....(ii)

Subtracting (ii) from (i), we get

AB²−AC²=BD²−CD²

⇒ AB²+CD² =AC ² +BD ²

[Hence proved]

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