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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asked Jun 12 in Class VII Maths by muskan15 (-3,451 points)

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

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answered Jun 12 by aditya23 (-2,194 points)

(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

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