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True or False: If the three angles of one triangle equal the three angles of another, the triangles must be congruent.

Class 9Triangles (Congruence)Geometry — Triangles
  • AFalse — equal angles only make them similar
  • BTrue — equal angles fix the triangle
  • CTrue, but only for right triangles
  • DFalse — two triangles can never have equal angles

Step-by-Step Solution

Equal angles only make the triangles similar (same shape). They can differ in size, so they need not be congruent.
Answer: A) False — equal angles only make them similar

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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