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To find the height of a brick-kiln chimney, Anjali lays a small mirror flat on the ground 18 m from its base and steps back until she can see the top of the chimney in the mirror. She is then 2 m behind the mirror and her eyes are 1.5 m above the ground. Taking the two triangles formed at the mirror as similar, find the height of the chimney.

Class 10Triangles (Similarity)Geometry — Similarity
  • A24 m
  • B27 m
  • C12 m
  • D13.5 m

Step-by-Step Solution

The mirror makes the two right triangles similar, so , i.e. , so m. 24 m comes from turning the ratio upside down ; 27 m from multiplying by 1.5 and forgetting to divide by 2; 12 m from dividing 18 by 1.5.
Answer: D) 13.5 m

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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