- ASSS
- BAAS
- CSAS
- DRHS
Step-by-Step Solution
AAS (Angle-Angle-Side) uses two angles and a non-included side. It follows from ASA because the third angle is fixed by the angle-sum property.
Answer: B) AAS
If two angles and one side of a triangle equal two angles and the corresponding side of another triangle, they are congruent. This rule (when the side is non-included) is called:
Class 9Triangles (Congruence)Geometry — Triangles
Key idea: The four valid congruence criteria
**SSS**: All three sides equal → congruent.
**SAS**: Two sides + included angle equal → congruent.
IMPORTANT: the angle must be BETWEEN the two given sides. SSA (two sides + non-included angle) is NOT a valid criterion in general.
**ASA**: Two angles + included side equal → congruent.
**AAS**: Two angles + a non-included side equal → congruent (since the third angle is forced by 180°).
**RHS** (right triangles only): Right angle + hypotenuse + one side equal → congruent.
**Once congruent, all corresponding parts are equal (CPCT)** — that's the lemma you cite to extract any matching side or angle in the next step of a proof.
**SAS**: Two sides + included angle equal → congruent.
IMPORTANT: the angle must be BETWEEN the two given sides. SSA (two sides + non-included angle) is NOT a valid criterion in general.
**ASA**: Two angles + included side equal → congruent.
**AAS**: Two angles + a non-included side equal → congruent (since the third angle is forced by 180°).
**RHS** (right triangles only): Right angle + hypotenuse + one side equal → congruent.
**Once congruent, all corresponding parts are equal (CPCT)** — that's the lemma you cite to extract any matching side or angle in the next step of a proof.
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