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Assertion (A): Two triangles whose three angles are equal, one to one, must have equal areas. Reason (R): Equal angles make two triangles similar, and similar triangles need not be of the same size. Choose the correct option.

Class 10Triangles (Similarity)Geometry — Similarity
  • 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 but R is false
  • DA is false but R is true

Step-by-Step Solution

Equal angles give similarity (AA), not congruence — a triangle and an enlarged copy of it have the same angles but different areas, so A is false. R states the correct fact and is true; in fact R is exactly the reason why A fails.
Answer: D) A is false but R is true

Key idea: Similarity vs congruence

**Congruent**: same shape AND same size. All corresponding parts equal.
**Similar**: same shape, possibly DIFFERENT size. Corresponding angles equal; corresponding sides PROPORTIONAL (in fixed ratio k).

If two triangles are similar with scale factor :
- Corresponding sides differ by factor .
- Corresponding angles are equal (always, by definition).
- Areas differ by factor — critical fact, and a common test question.

**Examples**:
- Equilateral triangles are ALL similar (same angles 60°-60°-60°).
- A photograph and its enlarged print are similar.
- Two right triangles sharing one acute angle are similar (AA).

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