Course Guide - USAID Teacher Education Project

c) On a sheet of plain paper, have students draw two 20 cm. intersecting lines (a large"X"). It is not necessary that the lines intersect at their halfway points. Rather, it ispreferable for the understanding of similar triangles that the lines cross at a pointother than the halfway point, such as:Once students have done this, have them join the endpoints as shown above. What dothey notice about the two triangles they have created?Next, have them fold the paper on the point of intersection and hold it up to the light.The two triangles will be overlapping. What do they notice now? Why is this so?As you listen to their explanations, help students move toward mathematically preciseterminology:1) The “vertical angles” (a new term introduced here) created by intersectinglines are equal.2) The principle of corresponding-side-angle-corresponding-side is a way ofconfirming similarity.(These are formal, secondary school ways of discussing similarity. However, preserviceteachers should be able to justify similarity in this way even though they willdescribe it in simpler terms for children.)