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Assertion (A): An equilateral triangle is also isosceles.
Reason (R): An isosceles triangle has at least two equal sides. Which is correct?

Class 9Triangles (Congruence)Geometry — Triangles
  • ABoth A and R are true, and R correctly explains A
  • BBoth A and R are true, but R does not explain A
  • CA is true, R is false
  • DA is false, R is true

Step-by-Step Solution

An equilateral triangle has three equal sides, so it certainly has at least two equal sides — it satisfies the isosceles definition. R is the exact reason A holds.
Answer: A) Both A and R are true, and R correctly explains A

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.

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