Florida B.E.S.T. MA.912.GR.1.2
The Standard
Prove triangle congruence or similarity using Side-Side-Side, Side-Angle-Side, Angle-Side-Angle, Angle-Angle-Side, Angle-Angle and Hypotenuse-Leg.
Florida B.E.S.T. Standards for Mathematics
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students match corresponding sides and angles in two triangles. They decide whether the given facts prove congruence, similarity, or neither, then justify the conclusion with a valid criterion.
What Mastery Looks Like
- Students select a valid criterion, match corresponding vertices, and support each claim with given facts. They use the proven relationship to find missing side lengths or angle measures.
Common Misconceptions
- Students may treat SSA or three matching angles as proof of congruence. They may pair the wrong vertices or write side ratios in inconsistent orders. Some trust the diagram’s appearance instead of marked facts.
How to Assess It
- Exit ticket: Triangle ABC has side lengths 6, 8, 10, and triangle DEF has side lengths 9, 12, 15. Decide whether they are congruent, similar, or neither, then state the criterion and correspondence.
Lesson moves
Ways to Teach It
Build triangles from given side and angle measurements using straws and protractors, then overlay them to test whether one unique shape is forced.
Write a short argument explaining why three equal angles prove similarity but not congruence, then compare explanations with a partner.
Play a card sort matching triangle diagrams with SSS, SAS, ASA, AAS, AA, HL, or insufficient information.
Measure a flagpole’s shadow and a meter stick’s shadow, then use similar triangles to calculate the flagpole’s height.
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Related Standards
- MA.8.GR.1.3
Use the Triangle Inequality Theorem to determine if a triangle can be formed from a given set of sides. Use the converse of the Pythagorean Theorem to determine...
- MA.8.GR.1.4
Solve mathematical problems involving the relationships between supplementary, complementary, vertical or adjacent angles.
- MA.912.GR.1.3
Prove relationships and theorems about triangles. Solve mathematical and real-world problems involving postulates, relationships and theorems of triangles.
- MA.912.T.1.5
Prove Pythagorean Identities. Apply Pythagorean Identities to calculate trigonometric ratios and to solve problems.
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