U3L5 Splitting Triangle Sides with Dilation, Part 1

In previous lessons, students reasoned about dilations and confirmed their properties. In this lesson, students use the definition of dilation to prove that the triangles formed by connecting midpoints of two sides are dilations of the original triangle. Then they deduce properties of these segments using a new line of argument: proving that two figures are dilations of one another is a way to prove the figures have properties of dilations (MP3). This prepares students to prove that pairs of triangles with certain properties must be dilations of one another, and therefore must be similar triangles. Note that in a later lesson, students will prove the converse of the theorems they explore 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. This activity includes lesson summary videos and practice problems

By JOEL NELSON