Regular pentagons have five points of rotational symmetry that you can demonstrate by rotating them 72, 144, 216 and 288 degrees from the starting point (which is the fifth point of rotational symmetry, 0 degrees). The best way to make this rotation clear to a math class is to draw a line from one vertex of a pentagon to its centroid. As you rotate the pentagon through the five positions where its outline looks identical, the line will rotate at 72-degree intervals to distinguish the five positions.
- Regular pentagon made of cardboard, foam core or similar
- Pencil
- Ruler
- Eraser
- Marker
- Cork board
- Push pin
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Instructions
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1
Measure and mark the midpoints of two edges of the pentagon.
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2
Draw a light pencil line from each midpoint you marked to the vertex opposite from it. Mark the centroid of the pentagon, where the two lines cross, with a dot using the marker. Erase the pencil lines.
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3
Draw a line in marker from the center point to one vertex of the pentagon.
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4
Push a pin through the center point of the pentagon and into a piece of cork board.
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5
Turn the pentagon in 72 degree increments to demonstrate the rotational symmetry of a regular pentagon.