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A figure is formed by drawing all the diagonals of a regular pentagon. How many lines of symmetry does this figure have?

hard MCQ 3 marks Class 7 · Mathematics · Symmetry
  1. 5
  2. 10
  3. 15
  4. 20
Answer
5

The correct answer is 5 — Therefore the figure has 5 lines of symmetry.

Step-by-step solution

  1. Drawing all diagonals of a regular pentagon produces a pentagram and a smaller inner pentagon.
  2. The resulting figure still retains the same rotational and reflectional symmetries as the original pentagon.
  3. A regular pentagon has exactly 5 lines of symmetry.
  4. No additional symmetry lines are introduced by the diagonals.
  5. Therefore the figure has 5 lines of symmetry.
Common mistake: Assuming each diagonal adds an extra symmetry line

Concept tested: Symmetry of complex polygons formed by diagonals

Published · How this solution was prepared and checked

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