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?

Solution

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.

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