Lesson 13: Congruence
About this lesson
So far, we have mainly looked at congruence for polygons. Polygons are special because they are determined by line segments. These line segments give polygons easily defined distances and angles to measure and compare. For a more complex shape with curved sides, the situation is a little different (unless the shape has special properties such as being a circle). The focus here is on the fact that the distance between any pair of corresponding points of congruent figures must be the same. Because there are too many pairs of points to consider, this is mainly a criterion for showing that two figures are not congruent: that is, if there is a pair of points on one figure that are a different distance apart than the corresponding points on another figure, then those figures are not congruent.
One of the mathematical practices that takes center stage in this lesson is MP6. For congruent figures built out of several different parts (for example, a collection of circles) the distances between all pairs of points must be the same. It is not enough that the constituent parts (circles for example) be congruent: they must also be in the same configuration, the same distance apart. This follows from the definition of congruence: rigid motions do not change distances between points, so if figure 1 is congruent to figure 2 then the distance between any pair of points in figure 1 is equal to the distance between the corresponding pair of points in figure 2.
Lesson overview
 13.1 Warmup: Not Just the Vertices (5 minutes)

13.2 Activity: Congruent Ovals (10 minutes)
 Includes "Are you Ready for More?" extension problem
 13.3 Activity: Corresponding Points in Congruent Figures (15 minutes)
 13.4 Optional Activity: Astonished Faces (10 minutes)
 Lesson Synthesis
 13.5 Cooldown: Explaining Congruence (5 minutes)
Learning goals:
 Determine whether shapes are congruent by measuring corresponding points.
 Draw and label corresponding points on congruent figures.
 Justify (orally and in writing) that congruent figures have equal corresponding distances between pairs of points.
Learning goals (student facing):
 Let’s find ways to test congruence of interesting figures.
Learning targets (student facing):
 I can use distances between points to decide if two figures are congruent.
Required materials:
 geometry toolkits
Glossary:
 Access the complete Grade 8 glossary.
IM 6–8 Math was originally developed by Open Up Resources and authored by Illustrative Mathematics, and is copyright 20172019 by Open Up Resources. It is licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0). OUR's 6–8 Math Curriculum is available at https://openupresources.org/mathcurriculum/.
Adaptations and updates to IM 6–8 Math are copyright 2019 by Illustrative Mathematics, and are licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0).
Adaptations to add additional English language learner supports are copyright 2019 by Open Up Resources, and are licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0).
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