- AYes, by RHS
- BNo, need more info
- CYes, by SSA
- DYes, by AAA
Step-by-Step Solution
Right angle + equal hypotenuse + one equal side → RHS criterion, so the triangles are congruent.
Answer: A) Yes, by RHS
Two right triangles have hypotenuse 10 cm and one leg 6 cm. Are they congruent?
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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