Lesson 2: 4-2: Congruent Triangles

1. What combination of rigid motions could you use to show that two polygons are congruent?
2. How can you use marks on polygons to determine which vertices are corresponding?
3. Why do you need to consider the sides of the polygons as well as the angles when using corresponding parts to prove that the polygons are congruent?

Principle of Superposition
Congruent Polygons
Corresponding Parts

G.CO.7
Use the definition of congruence in terms of rigid motions to show that two triangles are congruent if and only if corresponding pairs of sides and corresponding pairs of angles are congruent.
G.CO.10
Prove theorems about triangles
G.SRT.5
Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures.

https://docs.google.com/document/d/1Wi6oBP9pbwdBW1CPr4x4vVBOYkSXVKTdszWiPd1Ccm4/copy?usp=sharing

Two triangles are congruent if and only if their corresponding parts are congruent. Congruence can also be defined in terms of rigid motions. Two triangles are congruent if and only if one triangle can be mapped exactly onto the other by a rigid motion or a series of rigid motions. Congruence of triangles like that of angles and segments is reflexive, symmetric, and transitive.
Mathematically proficient students look for general methods while maintaining oversight of the process, while attending to the details.

As an antitheft device, many manufacturers make car stereos with removable faceplates. The shape and size of the faceplate and of the space where it fits must be exactly the same for the faceplate to properly attach to the car's dashboard.

Students should be careful with the difference between congruent polygons and similar polygons. In congruent polygons, all of the sides and angles have the same measure. If only the angles are shown to be congruent, this only proves that the polygons are similar, not congruent.

Students approaching grade level can be given practice problems in small groups to work with other students or directly with the teacher.
Students beyond grade level can make deeper connections by looking at two triangles in the coordinate plane. using the coordinates of the vertices, students can investigate how to prove the three pairs of sides are congruent to one another.

Formative Assessment

Textbook in class

Access online textbook and resources through class link.