Proving Triangles CongruentFive shortcuts that work, and the two that look like they…9th GradeTwo triangles are congruent if you canestablish any one of these five combinationsof equal parts.SSS · SAS · ASA · AAS · HLSSSthree sides equalRigid — only one triangle is possible.SAStwo sides and the angle betweenThe angle must be between the two sides.ASA / AAStwo angles and a sideThe side's position matters for naming, not for validity.HLright triangles onlyHypotenuse and one leg.THE COMMON MISTAKE✗ SSA proves congruence✓ SSA does notTwo different triangles can share two sides and a non-included angle. It is called the ambiguous case.AAA proves similarity, never congruence — the shapes match but thesizes need not.Proving Triangles Congruentwww.littleactivity.com

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Math · 9th Grade

Proving Triangles Congruent

Five shortcuts that work, and the two that look like they should but do not.

How to use it

Mark the given information on the diagram before writing a single line of proof.

Free · print-ready PDF · US Letter and A4

Grade
9th Grade
Ages
14–15
Subject
Math
Pages
1

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