Module 2, Topic B is a critical foundation to the understanding of congruence. All the lessons of Topic B demonstrate to students the ability to sequence various combinations of rigid motions while maintaining the basic properties of individual rigid motions. Lesson 7 begins this work with a sequence of translations. Students verify experimentally that a sequence of translations has the same properties as a single translation. Lessons 8 and 9 demonstrate sequences of reflections and translations and sequences of rotations. The concept of sequencing a combination of all three rigid motions is introduced in Lesson 10; this paves the way for the study of congruence in the next topic.
In Module 2, Topic C, on the definition and properties of congruence, students learn that congruence is just a sequence of basic rigid motions. The fundamental properties shared by all the basic rigid motions are then inherited by congruence: congruence moves lines to lines and angles to angles, and it is both distance- and degree-preserving (Lesson 11). In Grade 7, students used facts about supplementary, complementary, vertical, and adjacent angles to find the measures of unknown angles (7.G.5). This module extends that knowledge to angle relationships that are formed when two parallel lines are cut by a transversal. In Topic C, on angle relationships related to parallel lines, students learn that pairs of angles are congruent because they are angles that have been translated along a transversal, rotated around a point, or reflected across a line. Students use this knowledge of angle relationships in Lessons 13 and 14 to show why a triangle has a sum of interior angles equal to 180˚ and why the exterior angles of a triangle are the sum of the two remote interior angles of the triangle.
In this interactive activity, students will be led through steps to identify congruent figures. There are teaching activities as well as practice activities available. A handout that describes strategies taught during the interactive is available to be printed. After utilizing this resource, the students can complete the short quiz to assess their understanding.
In this Desmos activity, students explore transformations of plane figures and describe these movements in everyday language using words like "slide," "shift," "turn," "spin," "flip," and "mirror." Students are not expected to use formal math vocabulary yet. This lesson provides both the intellectual need for agreeing upon a common language and the chance for students to experiment with different ways of describing some transformations in the plane. This activity should be used to help teach a lesson on transformations. This Desmo activity offers sample student responses and a teacher guide.
This Custom Polygraph is designed to spark vocabulary-rich conversations about transformation. Key vocabulary that may appear in student questions includes translation, rotation, reflection, dilation, scale factor, pre-image, and image. In the early rounds of the game, students may notice graph features from the list above, even though they may not use those words to describe them. After most students have played 2-3 games, consider taking a short break to discuss strategy, highlight effective questions, and encourage students in their use of increasingly precise academic language. This activity should be used to help teach a lesson on transformations. This Desmos activity offers sample student responses and a teacher guide.