Similar Triangles 

Two triangles are similar if all three angles of one triangle are congruent to the corresponding ones of  the other. In layman’s terms, two triangles are similar if they have same shape but not necessarily same size.

Proving Two Triangles Are Similar

However, to prove two triangles are similar, we don’t need to show all three pairs of corresponding angles are congruent. We only need to show two pairs. This is called AA (angle-angle) postulate:

If two angles of one triangle are congruent to the two corresponding angles of another triangle, then these two triangles are similar.

We don’t need to show the last pair of angles are congruent because they will be congruent automatically.

Properties of Similar Triangles

Once you know the two triangles are similar, their corresponding sides will be proportional. That is, if DABC ~ DDEF (the symbol ~ means similar),

then