G.3.5.3 A Little Bit Farther Now

Here’s a triangle ABC. M is 2/3 of the way from A to B. N is 2/3 of the way from A to C. What can you say about segment MN, compared to segment BC? Provide a reason for each of your conjectures.

The triangles formed by connecting midpoints of sides of the triangle are just a special case of dilating triangles using one vertex as the center, but it has some cool properties, which is why we studied it. What specifically does it tell you about the shapes if one is a dilation of the other?