In Grade 8, students informally showed that a dilation maps a segment to a segment on the coordinate plane. The lesson includes an opening discussion that reminds students of this fact. Next, students must consider how to prove that dilations map segments to segments when the segment is not tied to the coordinate plane. We again call upon our knowledge of the triangle side splitter theorem to show that a dilation maps a segment to a segment. The goal of the lesson is for students to understand the effect that dilation has on segments, specifically that a dilation will map a segment to a segment so that its length is times the original.
To complete the lesson in one period, it may be necessary to skip the opening discussion and Example 4 and focus primarily on the work in Examples 1–3. Another option is to extend the lesson to two days so that all examples and exercises can be given the time required to develop student understanding of the dilation of segments.