Florida B.E.S.T. MA.912.GR.2.7
The Standard
Justify the criteria for triangle congruence using the definition of congruence in terms of rigid transformations.
Florida B.E.S.T. Standards for Mathematics
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students use translations, rotations, and reflections to line up two triangles. They explain why given side and angle conditions force every corresponding point to match. They connect that reasoning to SSS, SAS, ASA, AAS, and hypotenuse-leg criteria.
What Mastery Looks Like
- Given a pair of triangles, a student identifies a valid criterion and describes transformations mapping one triangle onto the other. The student explains why the measurements allow no alternate triangle and rejects AAA and SSA with counterexamples.
Common Misconceptions
- Students may think equal angle measures prove congruence, although AAA only fixes shape. They often accept SSA, overlook ambiguous cases, or match noncorresponding parts. Some rely on how a sketch looks instead of the marked facts.
How to Assess It
- Exit ticket: In triangles ABC and DEF, AB = DE, AC = DF, and ∠A = ∠D. Name the criterion, describe rigid motions mapping ABC onto DEF, and explain why B and C must land on E and F.
Lesson moves
Ways to Teach It
Give pairs of paper triangles and tracing paper; students translate, rotate, and reflect one triangle, then label the measurements that forced the match.
Ask students to write why SAS fixes a unique triangle, then compare it with an SSA example that produces two triangles.
Run a card sort with cards labeled SSS, SAS, ASA, AAS, AAA, and SSA; students place each under proves or does not prove.
Show two triangular roof braces with marked lengths and angles; students decide whether one template can verify both braces are congruent.
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Related Standards
- MA.912.GR.2
Apply properties of transformations to describe congruence or similarity.
- MA.912.GR.2.9
Justify the criteria for triangle similarity using the definition of similarity in terms of non-rigid transformations.
- MA.912.GR.2.6
Apply rigid transformations to map one figure onto another to justify that the two figures are congruent.
- MA.912.GR.1.2
Prove triangle congruence or similarity using Side-Side-Side, Side-Angle-Side, Angle-Side-Angle, Angle-Angle-Side, Angle-Angle and Hypotenuse-Leg.
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