Question

In the figure,AD// BC,AD= BC. Prove that:Triangle ADB is congurent to Triangle DBC.

Answer 1

see the figure ,
AD || BC ,
So, ∠ABD = ∠BDC
and , ∠ADC = ∠DBC
given, BD is common side of both Δ
we know, according to rule of ASA of congruence.
ΔADB ≌ ΔDBC

Answer 2

Here we have to show ∆ABD~∆DBC
so here are the conditions,
1- AD=BC
2- angle ADB=Angle DBC
3- BD is common side.

So both triangles are similar(by S-A-S)

Thanks.
Tripathy