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Question
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
Solution
(i) In the given figure Δ ABC
AD ⊥ BC, BD = CD
In Δ ABD and Δ ACD
AD = AD ............(common)
∠ADB = ∠ADC ...............(each 90°)
BD = CD ...........(Given)
∴ Δ ABD ≅ Δ CAD .........(By SAS Rule)
(ii) Side AB = AC .........(c.p.c.t.)
(iii) ∠B = ∠C
Reason, since Δ ADB ≅ Δ ADC
∴ ∠B = ∠C
Hence proved.
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