How do you prove two lines are parallel given (basically) a triangle on top of a trapezoid? The two bottom angles of both the triangle and the trapezoid are congruent.
+130513 I assume that you want to show that the base of the triangle [ or top of the trapezoid] is parallel to the bottom side of the trapezoid.
Since the base angle of the triangle and the trapezoid are congruent, these are corresponding angles cut by a transversal formed by the side of the trapezoid and the side of the triangle. And lines cut by a transversal such that their corresponding angles are equal are themselves parallel.
