Question

im the given figure AD =BD,Prove that BD <AC

Answer 1

There is a rule for this sum is-
Largest angle is equal to the opposite side is longest
Hope it will help you

Answer 2

Given: AD is the bisector of ∠BAC.
As AD is the bisector of ∠BAC.
∠BAD = ∠CAD …(1)
∠ADB > ∠CAD (exterior angle of a triangle is greater than each of opposite interior angle)
Then ∠ADB > ∠BAD (from (1))
⇒ AB > BD (opposite sides to greater angle is greater)
Hence proved.