FocusProving triangle congruence using SSS, SAS, and ASA, with a reason provided for every correspondence and conclusion.
Materials & Prep
Congruence proof practice set with two teacher-worked examples and multiple independent proofs, diagram copies, ruler, highlighters, and exit ticket.
Opening
5 minContentTriangle congruence means corresponding sides and angles are congruent, and corresponding vertices must be matched in the same order. The valid criteria in this lesson are SSS, SAS, and ASA. A proof requires statements supported by givens, definitions, properties, or a congruence theorem.
Student taskAnnotate a sample diagram by identifying corresponding vertices and classifying the available information as SSS, SAS, or ASA.
EvidenceAnnotated diagram and criterion classification.
Worked examples
12 minContentWorked example 1, SSS: Given AB ≅ DE, BC ≅ EF, and AC ≅ DF. Therefore, triangle ABC ≅ triangle DEF by SSS, with the correspondence A ↔ D, B ↔ E, and C ↔ F. Worked example 2, SAS: Given JK ≅ MN, JL ≅ MP, and angle J ≅ angle M. Therefore, triangle JKL ≅ triangle MNP by SAS because the congruent angle is included between the two congruent sides. Each statement is paired with a reason, including Given and the applicable congruence theorem.
Student taskComplete two proof organizers by recording the correspondence, matching givens to the diagram, identifying the included angle when needed, and writing the conclusion with its reason.
EvidenceTwo completed proof organizers with correct correspondence, criterion selection, and statement-reason pairs.
Guided practice
8 minContentASA proof structure using a shared side or explicitly given side. Example: If angle P ≅ angle S, PQ ≅ ST, and angle Q ≅ angle T, then triangle PQR ≅ triangle STR by ASA when the side lies between the two known angles in the correspondence. Proofs distinguish ASA from AAS by locating the known side between the known angles.
Student taskSolve one ASA proof and one classification item that requires distinguishing ASA from AAS or SAS.
EvidenceCompleted ASA proof and accurate criterion classification with written justification.
Independent practice
20 minContentMixed proof cases requiring SSS, SAS, and ASA. Problems include directly marked congruent parts, vertical angles, shared sides, and reflexive congruence. Each proof requires a correspondence statement, a sequence of statements and reasons, and a final triangle-congruence conclusion.
Student taskComplete four independent proofs: one SSS, one SAS, one ASA, and one that uses a vertical angle or a shared side as an additional reason. For each, identify the criterion before writing the conclusion.
EvidenceIndividual practice set showing correctly matched vertices, valid use of givens and geometric properties, accurate theorem selection, and justified final conclusions.
Exit assessment
5 minContentA final mixed proof requiring students to infer a shared-side or vertical-angle relationship and complete the congruence argument using the appropriate theorem.
Student taskComplete one proof independently and label the congruence criterion used.
EvidenceExit ticket with a logically ordered proof, a reason for every step, correct correspondence, and an accurate SSS, SAS, or ASA conclusion.
Assessment criteriaProficient work identifies corresponding vertices consistently, uses only valid congruence information, distinguishes SSS, SAS, and ASA accurately, places an included angle or side correctly when required, provides a mathematically valid reason for every step, and states the final congruence correspondence in the correct order.
DifferentiationA step-labeled proof organizer and reduced problem set support students who need structure; an extension set includes proofs requiring multiple inferred relationships and asks students to explain why an invalid criterion such as SSA cannot establish congruence.