Mathematics
ABC and DBC are two isosceles triangles on the same base BC. Show that ∠ABD = ∠ACD.
Triangles
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Answer
Given :
ABC and DBC are isosceles triangles.
Join AD.
In △ DAB and △ DAC,
⇒ AB = AC (Given)
⇒ BD = CD (Given)
⇒ AD = AD (Common side)
∴ △ ABD ≅ △ ACD (By S.S.S. congruence rule)
We know that,
Corresponding sides of congruent triangles are equal.
∴ ∠ABD = ∠ACD (By C.P.C.T.)
Hence, proved that ∠ABD = ∠ACD.
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