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G-CO.8 Warmup M1-043-A15-V03

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 \(\angle~A\cong~\angle~D\), \(\angle~B\cong~\angle~E\), \(AB\cong~DE\), and \(AC\cong~DF\). Determine every valid congruence criterion formed from exactly \(\text{three}\) marked facts and state each fact set.

Source facts: A↔D, B↔E, C↔F; ∠A≅∠D, ∠B≅∠E, AB≅DE, AC≅DF. 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