Symmetry Math Example 2

Follow the full solution, then compare it with the other examples linked below.

Example 2

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How many lines of symmetry does a regular pentagon have? Explain your reasoning.

Solution

  1. 1
    Step 1: A regular pentagon has 5 equal sides and 5 equal angles.
  2. 2
    Step 2: For any regular polygon with nn sides, the number of lines of symmetry equals nn.
  3. 3
    Step 3: Each line of symmetry in a regular pentagon connects one vertex to the midpoint of the opposite side.
  4. 4
    Step 4: Therefore a regular pentagon has 55 lines of symmetry.

Answer

5 lines of symmetry.
A regular nn-gon always has exactly nn lines of symmetry. Each line either connects two opposite vertices (for even nn) or connects a vertex to the midpoint of the opposite side (for odd nn, as with the pentagon).

About Symmetry

A geometric property where a figure remains unchanged under a specific transformation such as reflection, rotation, or translation. A shape has reflection symmetry when a line divides it into two mirror-image halves, and rotational symmetry when it looks the same after turning by a certain angle.

Learn more about Symmetry →

More Symmetry Examples

Example 1 easy

Does a square have a line of symmetry? Draw and describe one.

Example 3 easy

Does the letter 'A' have a line of symmetry? If so, describe it.

Example 4 hard

A shape has rotational symmetry of order 3. What is the smallest angle you can rotate it so it looks

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