Question

D is any point on side AC of a triangle ABC with AB=AC. show that CD is lesser than BD

Answer 1

Given - AB = AC

To prove -- BD > CD

Proof -- Since AB = AC
∠ABC = ∠ACB  (By Isosceles Triangle property) ----(i)

Here clearly,
∠ABC > ∠CBD 
∠ACB > ∠CBD ---from (i)
∠DCB > ∠CBD
BD > CD   (Angle opposite to greater side is greater in a triangle)

Hence Proved!

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