# The given figure shows a triangle ABC in which AD is perpendicular to side BC and BD = CD. prove that: ∆ABD ≅ ∆ACD

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The given figure shows a triangle ABC in which AD is perpendicular to side BC and BD = CD. Prove that:
(i) ∆ABD ≅ ∆ACD
(ii) AB=AC
(iii) ∠B = ∠C

answered 6 days ago by (-854 points)

(i) In the given figure △ABC

AD ⊥ BC, BD = CD

In △ ABD and △ACD

BD = CD (Given)

∴ △ABD △CAD (BY SAS Rule)

(ii) Side AB = AC (c.p.c.t)

(iii) ∠B = ∠C

∴ ∠B = ∠C

Hence proved