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Kabir stands 33 m from a building in Pune. He places a mirror on the flat ground between them, 3 m from himself, and sees the top of the building in it. His eyes are 1.5 m above the ground. How tall is the building?

Class 10Triangles (Similarity)Geometry — Similarity
  • A16.5 m
  • B60 m
  • C15 m
  • D13.5 m

Step-by-Step Solution

The mirror is m from the building. Equal angles at the mirror make the two right triangles similar: m.
Answer: C) 15 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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