U3L4 Dilating Lines and Angles

In middle school, students confirmed experimentally some of the properties of dilations (dilations take angles to congruent angles and lines to parallel lines). In this lesson, students verify experimentally and assert that dilations take angles to congruent angles, and use this assertion to create a convincing argument that if dilations take angles to congruent angles, they must take lines to parallel lines (MP3). Students draw on their work with angles formed by parallel lines and transversals in an earlier unit to complete the proof. Students also examine what happens to lines through the center of dilation under dilation. They reason based on the definition of dilation that those lines don’t change under dilation. Verifying the properties of dilation prepares students to use those properties in proofs involving similarity, such as proving the Angle-Angle Triangle Similarity Theorem. This activity includes lesson summary videos and practice problems

By JOEL NELSON