Question

Two Triangles are similar if corresponding sides are in proportion and corresponding angles are equal. By satisfying one condition is enough to say that triangles are simiar?

Answer 1

Yes.
1) AAA similarity : If two triangles are equiangular( all three angles are equal to each other), then they are similar.
Example : In ΔABC and ΔDEF, ∠A = ∠D, ∠B = ∠E and ∠C= ∠F then ΔABC ~ ΔDEF by AAA criteria.

2) SSS similarity : If all the three corresponding sides of two triangles are proportional, then the two triangles are similar.
Example : In ΔXYZ and ΔLMN, XY = LM, YZ = MN and XZ = LN then
ΔXYZ ~ ΔLMN by SSS criteria.

Two triangles XYZ and LMN such that

XY/LM=YZ/MN=XZ/LN
Then the two triangles are similar by SSS similarity.

So, by one satisfying one condition, the 2 triangles can be proved similar.