Lesson 4: 4-4: Proving Triangles Congruent - ASA, AAS

1. Can you look at two triangles and determine if there are any corresponding sides or angles that based on information given?
2. How could you show that a pair of corresponding sides of two triangles are congruent?

Included Side

G.CO.8
Students will explain how the criteria for triangle congruence (ASA, SAS, and SSS) follow from the definition of congruence in terms of rigid motions.
G.CO.12
Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.)
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

The Angle-Side-Angle Postulate, written as ASA, and the Angle-Angle-Side, or AAS, Theorem can also be used to prove triangle congruence.
Mathematically proficient students understand and use stated assumptions, definitions, and previously established results in constructing arguments.

Competitive rowing, also called crew, involves two or more people who sit facing the stern of the both, with each rower pulling one or two oars. In high school competitions, a race - called a regatta - usually requires a body of water that is more than 1500 meters long. Congruent triangles can be used to measure distances that are not easily measured directly, like the length of a regatta course.

Students should be sure that when using the AAS Postulate, they are using the side that is not between the two angles.

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 showing a counterexample to show that SSA cannot be used to show triangles are congruent.

Formative Assessment

Textbook in class

Access online textbook and resources through class link.