Question

In the picture below, the sides of the two triangles are parallel:

Prove that they are similar:

Answer 1

Given: ΔABC and ΔDEF with AB || DE, AC || DF and EF || BC

∠ABC = ∠DEF, ∠BAC = ∠EDF and ∠ACB = ∠DFE (Corresponding angles)

Now in ΔABC and ΔDEF:

∠ABC = ∠DEF (Proved above)

∠BAC = ∠EDF (Proved above)

∠ACB = ∠DFE (Proved above)

As all the angles of the triangle are equal to the angles of the other triangle, both the triangles are similar.