We are given the medial triangle of a triangle. Let us label these line j, k, and m. In the following diagram we see that we are given the medial triangle as the green triangle and we want to construct the blue triangle given the three line segments of the medial triangle.
What do we notice about the relationship of the two triangles? It appears that the two triangles are similar. It also appears that the sides of the triangles are parallel to each other. I will use Geometer's Sketchpad to explore these relationships of these triangles.
Are the triangles similar?
Are the lines parallel?