Unit 1, Lesson 12
Congruent Polygons
Grade 8
Preparation
Lesson Narrative
In this lesson, students find rigid transformations that show two figures are congruent and consider why two figures are not congruent. As students compare features of two shapes on a coordinate plane, they observe that having corresponding side lengths that are equal is not enough to determine that two figures are congruent. Students use differences in features, such as angle measures, side lengths, perimeters, or the order of congruent sides, to construct arguments that two figures are not congruent (MP3). Students also use the structure of the coordinate plane to compare features of two figures and identify rigid transformations precisely (MP7).
The last activity in the lesson is optional. It gives students an opportunity to apply the work from previous activities and to think more deeply about the conditions of congruence. At this time, students do not use congruent corresponding parts to justify congruence. They will have opportunities in later lessons to develop this idea as a consequence of their understanding of transformations.
- Critique arguments (orally) that two figures with congruent corresponding sides may be non-congruent figures.
- Justify (orally and in writing) that two polygons on a grid are congruent using the definition of "congruence" in terms of rigid transformations.
Let’s decide if two figures are congruent.
Required Materials
Activity 1
Activity 2
Activity 3
Required Preparation
If using this optional activity, have sets of objects ready for students to build quadrilaterals. Each pair of students requires 12 objects (such as toothpicks, pencils, or straws) to be used as sides of quadrilaterals: 8 objects of one length and 4 objects of a different length.