We can prove it by AAA or SSS similarity of triangles.

If in two triangles,

1. the corresponding angles are equal, then their corresponding sides are proportional (i.e. in the same

ratio) and hence the triangles are similar.

In two triangles ABC and DEF are similar, if

∠A = ∠D, ∠B = ∠E, ∠C = ∠F and AB/DE = BC/EF = CA/FD

In such a case, we write ΔABC ~ ΔDEF

1. AAA similarity: If two triangles are equiangular( all three angles are equal to each other), then they

are similar.

Ex: In ΔABC and ΔDEF, ∠A = ∠D, ∠B = ∠E and ∠C= ∠F then ΔABC ~ ΔDEF by AAA criteria.

2. SSS similarity: If the corresponding sides of two triangles are proportional, then the two triangles are

similar.

Ex: 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.