In this lesson, students continue to apply the concept of corresponding parts. In a previous lesson, students justified that two figures being congruent guarantees that all pairs of corresponding parts are congruent. In this lesson, students explore a different direction. If any pair of corresponding parts is not congruent, then the two figures cannot be congruent. Students attend to precision (MP6) as they determine whether congruence statements about figures are true in the warm-up, and look for corresponding parts in the activities. Students continue working toward establishing triangle congruence shortcuts as they examine a set of congruent parts, Side-Side-Angle, that are not sufficient to establish the triangles as congruent.
Technology isn't required for this lesson, but there are opportunities for students to choose to use appropriate technology to solve problems. We recommend making technology available.
- Justify whether or not figures are congruent by reasoning about rigid transformations (in writing).
- Practice generating and comprehending congruence statements (orally and in writing) that establish corresponding parts.
- Let’s name figures in ways that help us see the corresponding parts.
- I can identify corresponding parts from a congruence statement.
- I can use rigid transformations to explain why figures are congruent.
- I can write a congruence statement.
For a rigid transformation that takes one figure onto another, a part of the first figure and its image in the second figure are called corresponding parts. We also talk about corresponding parts when we are trying to prove two figures are congruent and set up a correspondence between the parts to see if the parts are congruent.
In the figure, segment \(AB\) corresponds to segment \(DE\), and angle \(BCA\) corresponds to angle \(EFD\).