Lesson eLearning

A figure is formed by joining all the diagonals of a regular octagon. How many lines of symmetry does the resulting figure have?

medium 2 marks Class 7 · Mathematics · Symmetry
Answer
8

The correct answer is 8 — Thus the resulting figure has lines of symmetry.

Step-by-step solution

  1. A regular octagon is symmetric about all lines that pass through its centre and either a vertex or the midpoint of a side.
  2. Drawing all diagonals does not alter the symmetry, it only adds more lines inside the shape.
  3. The figure still retains the same axes of symmetry as the original octagon.
  4. Thus the resulting figure has lines of symmetry.
Common mistake: Believing that adding diagonals reduces the number of symmetry axes

Concept tested: Symmetry preserved when adding diagonals

Published · How this solution was prepared and checked

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