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Question:

In given figure, ABC and DBC are two isosceles triangles on the same base BC. Show that ∠ABD = ∠ACD.

Solution:

In△ABC, we haveAB=AC⇒∠ABC=∠ACB... (1)∣Since angles opposite to equal sides are equalIn△BCD, we haveBD=CD⇒∠DBC=∠DCB... (2)∣Since angles opposite to equal sides are equalAdding (1) and (2), we have∠ABC+∠DBC=∠ACB+∠DCB⇒∠ABD=∠ACD