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Which of the following pairs of triangles is ALWAYS similar?

Class 10Triangles (Similarity)Geometry — Similarity
  • AAny two right triangles
  • BAny two isosceles triangles
  • CAny two equilateral triangles
  • DAny two triangles of equal area

Step-by-Step Solution

All equilateral triangles have angles 60°-60°-60°, so they are always similar (AA). The other pairs are not always similar.
Answer: C) Any two equilateral triangles

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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