similar Triangle

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!

I guess you mean something like this.



They needn't be similar but generally are because the test makers test similar triangle concepts using such figures.
Let's say, if you are given that angle BAC = angle DBC, then using AA, you know that the two triangles are similar (Since 2 angles are the same, the third would be the same too and hence you will get similar triangles)

Now I understand . Thanks a lot to both of you ..

Hey Deb,

yes i got what u trying to interpret from the logic.

1) the situation u described need not be similar triangles, as for 2 triangles to be similar atleast two angles should be equal.


Mostly the test takers(specially in GMAT and MGMAT questions) will describe a situation which i have seen mostly is:

There is a triangle ABC right anlgd at B suppose.From B we draw a perpndicular to base AC at point D.Then the three traingles which are all right angled are similar to each other.

The above mentioned point is a very good catch.Will save time if u rmbr ths concept.

+1 kudo if my post helped.

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