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Assertion (A): Two squares of different sizes are always similar. Reason (R): All squares have equal corresponding angles and proportional corresponding sides. 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

All squares have all angles 90° and all sides equal, so corresponding sides are proportional. Both A and R are true and R is the correct explanation.
Answer: A) Both A and R are true, and R correctly explains A

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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