Symmetry Math Example 4

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

Example 4

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

Solution

  1. 1
    Step 1: Rotational symmetry of order 3 means the shape looks identical 3 times in one full 360° rotation.
  2. 2
    Step 2: Divide 360° by the order: 360°÷3=120°360° \div 3 = 120°.

Answer

120°120°
The minimum rotation angle for a shape with rotational symmetry of order nn is 360°/n360°/n. An equilateral triangle has order-3 rotational symmetry and looks the same after rotations of 120°, 240°, and 360°.

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 2 medium

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

Example 3 easy

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

← All Symmetry Examples Symmetry Concept