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G-CO.8 Warmup M1-043-A15-V02

Explain ASA, SAS, and SSS triangle congruence criteria from rigid-motion congruence.

Evaluate which congruence criterion is valid and efficient

Problem

For triangles \(ABC\) and \(DEF\) with \(A\leftrightarrow~D\), \(B\leftrightarrow~E\), \(C\leftrightarrow~F\), the marked facts are \(AB\cong~DE\), \(AC\cong~DF\), and \(\angle~B\cong~\angle~E\). Test this evidence against \(SSS\), \(SAS\), \(ASA\), \(AAS\), and \(HL\); state every valid criterion and describe the evidence pattern.

Source facts: A↔D, B↔E, C↔F; only AB≅DE, AC≅DF, and ∠B≅∠E are marked. Open full size
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Four variants of this problem type
Curriculum context
Course
Math I
Standard
G-CO.8
Category
Geometry
Domain
Congruence
Objective
Explain ASA, SAS, and SSS triangle congruence criteria from rigid-motion congruence.
Problem type
Evaluate which congruence criterion is valid and efficient