What are three ways you can prove that triangles are similar?

Two triangles are similar if:

• two pairs of corresponding angles are equal, or
• one pair of angles is equal, and the ratiOS of the lengths of sides adjacent to the angles are the same, or
• the lengths of the three pair of corresponding sides are in the same ratio.

For the first point, if two angles of one triangle are equal to two of the other, then the third angles = 180 - sum of the two, must be equal.