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Rotational Symmetry of Regular Polygons

Author:Kendra Garmon, Duane Runyan, azb, youngcar

Remember: Regular Polygons are polygons with EQUAL SIDES AND ANGLES.

Remember: Regular Polygons are polygons with EQUAL SIDES AND ANGLES.

Equilateral Triangle

Number of Rotational Symmetries

How many times does an EQUILATERAL TRIANGLE rotate onto itself until it is back to the beginning? Include the rotation 360°.

Select all that apply
  • A
  • B
  • C
  • D
Check my answer (3)

List Rotational Symmetries

Choose the list that includes all Rotational Symmetries for an EQUILATERAL TRIANGLE.

Select all that apply
  • A
  • B
  • C
  • D
Check my answer (3)

Square

Number of Rotational Symmetries

How many times does a SQUARE rotate onto itself until it is back to the beginning? Include the rotation 360°.

Select all that apply
  • A
  • B
  • C
  • D
Check my answer (3)

List Rotational Symmetries

Choose the list that includes all Rotational Symmetries for a SQUARE.

Select all that apply
  • A
  • B
  • C
  • D
Check my answer (3)

Number of Rotational Symmetries

How many times does a REGULAR PENTAGON rotate onto itself until it is back to the beginning? Include the rotation 360°.

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List Rotational Symmetries

Choose the list that includes all Rotational Symmetries for a REGULAR PENTAGON.

Select all that apply
  • A
  • B
  • C
  • D
Check my answer (3)

Point of Rotation

Where is the point of rotation in each of the applets above?

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Noticing Patterns

What do you notice about the number of times a regular polygon will rotate onto itself? What relationship do you see?

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Calculating Degrees of Rotational Symmetry

Given the number of sides of an object, and that each full rotation is 360 degrees, how could you determine each degree of rotation for any regular polygon?

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Image of a Regular Hexagon

Image of a Regular Hexagon
This image does not move. Use what you have learned to answer the following questions.

Number of Rotational Symmetries

Based on the patterns you described above, how many times does a REGULAR HEXAGON rotate onto itself until it is back to the beginning? Include the rotation 360°.

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List Rotational Symmetries

Using the pattern/formula you described earlier, list all degrees of rotation that will carry a REGULAR HEXAGON onto itself. (Only enter the numbers).

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Rotational symmetry of Non-regular polygons

What happens when we try to rotate a polygon onto itself that doesn't have equal sides and angles? Explore with a rectangle and trapezoid below.

Rectangle (non-regular polygon)

Number of Rotational Symmetries

How many times did the rectangle land onto itself?

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List Rotational Symmetries

What degrees of rotation landed a rectangle back onto itself? (Only enter the numbers)

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Number of Rotational Symmetries

How many times did the trapezoid land onto itself?

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List Rotational Symmetries

What degrees of rotation landed a trapezoid back onto itself? (Only enter the numbers)

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Summarize

Summarize in at least 3 sentences what you learned from this discovery applet. Include words such as regular polygon, non-regular polygon, rotational symmetry, sides, degrees of rotation, etc.

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