- ARHS
- BSAS
- CSSS
- DASA
Step-by-Step Solution
Both triangles are right-angled at and . The hypotenuses are equal , two ticks) and one more side is equal , one tick), so the rule is RHS.
Answer: A) RHS
Both triangles have a right angle (square marks). Using the tick marks, which rule proves △ABC ≅ △PQR?
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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