← MATH 01310 · College Geometry
MATH 01310 · Proof & congruence/similarity
Triangle congruence criteria
Definition
SSS, SAS, ASA, AAS (and HL for right triangles) guarantee triangle congruence. SSA is not a general congruence theorem (ambiguous case).
Read this
Congruent triangles: all corresponding sides and angles match. Order of vertices in naming shows correspondence (△ABC ≅ △DEF).
SAS needs the included angle; ASA needs the included side. AAS is equivalent via angle sum.
Never invent “AAA congruence” — AAA gives similarity, not congruence.
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Attempt each problem first, then open the worked solution.
1.Mark a figure and prove two triangles congruent by SAS, citing each reason.