Unit 2, Lesson 6
Side-Angle-Side Triangle Congruence
Geometry
Preparation
Lesson Narrative
In this lesson, students prove the Side-Angle-Side Triangle Congruence Theorem. That is, they justify that if two pairs of corresponding sides and the pair of corresponding angles between those sides are congruent, then there must be a sequence of rigid motions that takes one triangle exactly onto the other. Students are then given the opportunity to apply the theorem to prove the base angles are congruent in isosceles triangles.
Applying the Side-Angle-Side Triangle Congruence Theorem to an isosceles triangle involves purposefully drawing an additional line with certain properties. Drawing these auxiliary lines is an important way that mathematicians look for and make use of structure (MP7).
Technology isn’t required for this lesson, but there are opportunities for students to choose to use appropriate technology to solve problems. We recommend making technology available.
- Justify (in writing) the Side-Angle-Side Triangle Congruence Theorem.
- Prove (in writing) the Isosceles Triangle Theorem.