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Mathematics — CBSE Class 10 board question

Q1. [1]
Which of the following statements is incorrect ?
  1. A Two congruent figures are always similar.
  2. B A square and a rhombus of the same area are always similar.
  3. C Two equilateral triangles are always similar.
  4. D Two similar triangles need not be congruent.
Previously asked in CBSE board exam
2025 30/2/1 Q9
Generated by claude-sonnet-4-6 · 2026-06-15 10:36 · grounding rag
Model Answer

Answer: (B)

A square and a rhombus of the same area are not always similar, as their angles differ (a square has all 90° angles, a rhombus need not).

Explanation

Similarity requires both equal corresponding angles AND proportional sides. A rhombus has equal sides but its angles can vary, so it is not always similar to a square. The other three statements are correct: congruent figures are always similar (ratio 1:1); two equilateral triangles always have 60°-60°-60°; similar triangles need not be congruent. Examiners expect you to identify the false statement and briefly justify.

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