 Lesson plan

# Lesson 13: Congruence

teaches Alabama State Standards 8-22.
teaches Arizona State Standards 8.G.A.2
teaches Common Core State Standards MP3 http://corestandards.org/Math/Practice/MP3
teaches Common Core State Standards MP7 http://corestandards.org/Math/Practice/MP7
teaches Common Core State Standards MP6 http://corestandards.org/Math/Practice/MP6
teaches Common Core State Standards 8.G.A.1.a http://corestandards.org/Math/Content/8/G/A/1/a
teaches Common Core State Standards 8.G.A.2 http://corestandards.org/Math/Content/8/G/A/2
teaches Georgia State Standards MGSE8.G.2.
teaches Georgia State Standards MGSE8.G.1.
teaches New York State Standards NY-8.G.2.
teaches New York State Standards NY-8.G.1a.
teaches Ohio State Standards 8.G.2.
teaches Pennsylvania State Standards CC.2.3.8.A.2.

# Lesson 13: Congruence

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 Warm-up: 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 Cool-down: 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 2017-2019 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/math-curriculum/.