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Section: G.2.3

Triangle Congruence Criteria

• 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 (CPCTC).
• Explain how the criteria for triangle congruence follow from the definition of congruence.
• Prove that base angles of isosceles triangles are congruent.

Students build on their understanding of rigid motions to formalize the definition of congruence that they developed in grade 8. They specify a series of rigid motions that carries one figure onto another and use the definition to determine whether two objects are congruent. Students show two triangles are congruent if and only if corresponding pairs of sides and angles are congruent. They explain how the criteria for triangle congruence (ASA, SAS, SSS) follow from the definition of congruence in terms of rigid motions. Armed with these criteria, students are able to prove theorems about triangles, lines, angles, and parallelograms.

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Tasks

1 Properties of Congruent Triangles

2 Why does SAS work?

3 Why Does ASA Work?

4 When Does SSA Work to Determine Triangle Congruence?

5 Why does SSS work?

6 Angle bisection and midpoints of line segments

7 Congruent angles in isosceles triangles