NY Next Generation Math GEO-G.CO.8

MathGrades 9–12Understand congruence in terms of rigid motions.

The Standard

Explain how the criteria for triangle congruence (ASA, SAS, SSS, AAS and HL (Hypotenuse Leg)) follow from the definition of congruence in terms of rigid motions.

New York State Next Generation Mathematics Learning Standards

Teacher's field guide

What This Standard Means

What Students Need to Do

Students explain why ASA, SAS, SSS, AAS, and HL guarantee triangle congruence through rigid motions. They identify which measurements fix a triangle uniquely.

What Mastery Looks Like

The student selects a valid criterion from a diagram and describes how one triangle can be placed onto the other. The student rejects insufficient combinations such as SSA in general.

Common Misconceptions

Students may treat any three matching measures as sufficient or use HL for nonright triangles. They may confuse AAS with an unsupported SSA argument.

How to Assess It

Give four pairs of triangles with marked information. Ask which are guaranteed congruent, name the criterion, and justify one using rigid motions.

Lesson moves

Ways to Teach It

  1. Construct triangles from assigned side and angle sets to test which data create only one shape.

  2. Ask why SSA can produce two different triangles while SAS cannot.

  3. Play congruence criterion sort with diagrams labeled ASA, SAS, SSS, AAS, HL, or insufficient.

  4. Choose measurements that would verify two roof-truss triangles are congruent.

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