A triangle can be thought of as a trapezoid with one base of length zero. Then the two conclusions made are the same. In other words, the first conclusion regarding the triangle is a special case of the second conclusion regarding the trapezoid. The student understands the importance of logical reasoning, justification, and proof in mathematics. The student uses deductive reasoning to prove a statement.
Students repeat the process for other polygons.
They deduce a general formula for the sum of the angles of an n-sided convex polygon. Students can extend this activity to other polygons, making sure to draw the diagonals from only one vertex.