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Question

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

In ABC, we have
AB=AC
ABC=ACB... (1) Since angles opposite to equal sides are equal
In BCD, we have
BD=CD
DBC=DCB ... (2) Since angles opposite to equal sides are equal
Adding (1) and (2), we have
ABC+DBC=ACB+DCB
ABD=ACD


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