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
(i) In the given figure △ABC
AD ⊥ BC, BD = CD
In △ ABD and △ACD
AD = AD (Common)
∠ADB = ∠ADC (each 90%)
BD = CD (Given)
∴ △ABD ≅ △CAD (BY SAS Rule)
(ii) Side AB = AC (c.p.c.t)
(iii) ∠B = ∠C
Reasons, since △ADB ≅ △ADC
∴ ∠B = ∠C
Hence proved