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Question

ABCandDBC are two isosceles triangles on the same base BC. Show that ABD=ACD.


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Solution

Proving ABD=ACD:

In ABC,

AB=AC (ABC is isosceles triangle)

Therefore, ABC=ACB [angles opposite to equal sides are equal]…………(1)

In DBC,

DB=DC (DBC is isosceles triangle)

Therefore, DBC=DCB [angles opposite to equal sides are equal]………..(2)

Adding equations (1) and (2), we get

ABC+DBC=ACB+DCBABD=ACD

Hence Proved


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