Lesson 3: 4-3: Proving Triangles Congruent - SSS, SAS

1. Can two triangles be considered congruent if only five pairs of corresponding parts are congruent instead of all six?

Included Angle

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.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 Postulates that establish the Side-Side-Side congruence criterion (SSS) and the Side-Angle-Side congruence criterion (SAS) follow from the definition of congruence in terms of rigid motion. They are used to prove that two or more triangles are congruent.
Mathematically proficient students look for entry points into a solution. They plan a pathway rather than simply jumping into a solution attempt.

An A-frame sandwich board is a convenient way to display information. Not only does it fold flat for easy storage, but with each side arm locked into place, the frame is extremely sturdy. With the sidearms the same length and positioned the same distance from the top on either side, the open frame forms two congruent triangles.

Students should be sure that when they are using the SAS Postulate, the angle must be between the two adjacent sides.

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 answering questions around determining the difference of when to use one postulate over the other.

Formative Assessment

Textbook in class

Access online textbook and resources through class link.