Only thing which is sufficient to prove two triangle as similar is

"all the angles should be equal"

So does not matter whether they have a common base or not. If you can prove that all of their angles are equal then it's enough to say that they are similar triangles.

If

Angle ADB = Angle ADC

Angle ABD = Angle ACD

Angle BAD = Angle CAD

=> ABC and ABD are similar triangles....

Also there are other cases (but in these cases you will end up proving that both triangles are equivalent, (equivalent triangles are subset of similar triangles))

Possible cases:

1) Common base BC and the two attached angles...I.e. <ACB =<DCB and <ABC = <DBC

2) two sides and included sides are equal... I.e. AB = DB, BC = BC and <ABC = <DBC

In both of the cases we have equivalent triangles which will obviously be similar

Hope it helps!

_________________

Ankit

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