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Question

△ABC and △DBC are two isosceles triangles on the same base BC (see figure). Show that ∠ABD=∠ACD
569823_315d464372d2462b9390f9368c5755e0.png

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Solution

Given ΔABC and ΔDBC are two isosceles triangles on the same base BC


In isosceles ΔABC


AB=AC

Then ∠ABC=∠ACB................................(1)

In isosceles ΔBDC


BD=DC

Then ∠CBD=∠BCD..................................(2)

Add (1) and (2) we get

∠ABC+∠CBD=∠ACB+∠BCD

But ΔABC and ΔDBC on same base

∴∠ABD=∠ACD


714314_569823_ans_3f7820bf6bcc4d1a869da541466139c2.png


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