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G-CO.8 Warmup M1-043-A09-V04

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

Complete a missing proof statement or reason

Problem

Complete the missing reason in this proof step: \(\angle~M~=~\angle~Q,~MN~=~QR,~\text{and}~\angle~N~=~\angle~R\), so \(\triangle~MNO~\cong~\triangle~QRS\) by .

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△MNO ≅ △QRS by SSS because the triangles have matching corresponding parts.

△MNO ≅ △QRS by SAS because MN = QR and the two angle congruences complete side-angle-side.

△MNO ≅ △QRS by ASA because ∠M = ∠Q, MN = QR, and ∠N = ∠R give two angles and the included side.

△MNO ≅ △QRS by AAS because ∠M = ∠Q, MN = QR, and ∠N = ∠R give two angles and a side.

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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: Complete a missing proof statement or reason