n RD Sharma 's Maths page 4.3,Q.2(vi) state T/F for the statement All Triangles with proportionate angles are similar, the answer shown by you is TRUE. Please clarify the correctness of the answer.

Radha(parent)

Definition of Similar triangles:

Two triangles are said to be similar, if

(i) their corresponding angles are equal and,

(ii) their corresponding sides are proportional.

The statement holds because corresponding angles of two triangles are proportional only when corresponding angles are equal along with the fact that Angle-Sum property is satisfied.

Example:

Consider two triangles, ΔABC and  ΔDEF

where, for ΔABC, Let's say ∠A = 100°, ∠B = 50°, ∠C = 30° 

and for ΔDEF, ∠D = 50°, ∠E = 25°, ∠F = 15°

Now, no such case exist first of all because ΔDEF does not satisfy Angle-Sum property even when we can see that

∠A :∠D = 2:1, ∠B :∠E = 2:1, ∠C :∠F = 2:1

So, the statement remains always true because we cannot find any case that contradicts the given statement.