Look at the figure below: Triangle PQR has the measure of angle PRQ equal to 30 degrees. S is a point on side PR. Points Q and S are joined by a straight line. Angle PQS measures 30 degrees.

angle RPQ = angle SPQ                    (common angle to both triangles) angle PRQ = angle PQS                    (given) Hence, angle PQR = angle PSQ        (sum of angle of a triangle is 180 degrees) Since the angles of both triangles are equal, then the two triangles are similar.