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Learning Goal
Part of: Understand congruence in terms of rigid motions — 3 of 3 cluster items
Explain triangle congruence criteria
HSG.CO.B.8
**HSG.CO.B.8**: Explain how the criteria for triangle congruence (ASA, SAS, and SSS) follow from the definition of congruence in terms of rigid motions.
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HSG.CO.B.8: Explain how the criteria for triangle congruence (ASA, SAS, and SSS) follow from the definition of congruence in terms of rigid motions.
What you'll learn
- Explain why the SAS criterion (two sides and the included angle) is sufficient to guarantee triangle congruence, using the rigid-motion construction from CO.B.7
- Explain why the ASA criterion (two angles and the included side) is sufficient to guarantee triangle congruence, using rigid motions and the triangle angle sum property
- Explain why the SSS criterion (three sides) is sufficient to guarantee triangle congruence, using rigid motions and the properties of circle intersections
- Explain why certain combinations of parts — specifically SSA (two sides and a non-included angle) and AAA (three angles) — do NOT guarantee congruence, by constructing explicit counterexamples
- Use SAS, ASA, and SSS as efficient shortcuts for establishing triangle congruence in geometric proofs, replacing the need to verify all six pairs of corresponding parts
Prerequisites
Slides
Interactive presentations perfect for visual learners • 2 slide decks
Slide Video
Watch narrated slides play like a video lesson • Narrated slide playback
Exercises
Practice problems to build fluency and understanding • 1 exercises