In this lesson, students focus on triangles that are dilated using a vertex as the center of dilation. They begin by looking at the figure formed by connecting the midpoints of two sides of a triangle and write a convincing argument that this is a dilation of the original triangle (MP3). This allows students to use the properties of dilation to compare the two triangles, including the idea that the segment connecting midpoints must be parallel to a side of the original triangle.

Note that in a later lesson students will prove the converse of the ideas in this lesson–that a segment parallel to one side of a triangle divides the other two sides proportionally. If students notice or wonder about this fact, leave it as a conjecture for now.