Rotational Symmetry of Regular Polygons

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

Equilateral Triangle

Number of Rotational Symmetries

Does the [b]EQUILATERAL TRIANGLE[/b] rotate onto itself when rotated at 90°?

No Yes

List Rotational Symmetries

Choose the list that includes all Rotational Symmetries for an [b]EQUILATERAL TRIANGLE. (Angles at which it lines up with the original triangle)[/b]

90[math]^\circ[/math], 180[math]^\circ[/math], 270[math]^\circ[/math], 360[math]^\circ[/math][br] 120[math]^\circ[/math], 240[math]^\circ[/math], 360[math]^\circ[/math][br] None of these answers 60[math]^\circ[/math], 120[math]^\circ[/math], 180[math]^\circ[/math], 360[math]^\circ[/math]

Square

Number of Rotational Symmetries

Does the [b]SQUARE[/b] have 90° rotational symmetry?

No Yes

List Rotational Symmetries

Choose the list that includes all Rotational Symmetries for a [b]SQUARE. [b](Angles at which it lines up with the original square)[/b][/b]

120[math]^\circ[/math], 240[math]^\circ[/math], 360[math]^\circ[/math][br] 60[math]^\circ[/math], 120[math]^\circ[/math], 180[math]^\circ[/math], 360[math]^\circ[/math] 90[math]^\circ[/math], 180[math]^\circ[/math], 270[math]^\circ[/math], 360[math]^\circ[/math][br] None of these answers

Number of Rotational Symmetries

Does a [b]REGULAR PENTAGON[/b] have 90° rotational symmetry?

No Yes

List Rotational Symmetries

Choose the list that includes all Rotational Symmetries for a [b]REGULAR PENTAGON. [b](Angles at which it lines up with the original pentagon)[/b][/b]

72[math]^\circ[/math], 144[math]^\circ[/math], 216[math]^\circ[/math], 288[math]^\circ[/math], 360[math]^\circ[/math] 72[math]^\circ[/math], 180[math]^\circ[/math], 270[math]^\circ[/math], 360[math]^\circ[/math][br] 60[math]^\circ[/math], 120[math]^\circ[/math], 180[math]^\circ[/math], 360[math]^\circ[/math] 50[math]^\circ[/math], 100[math]^\circ[/math], 200[math]^\circ[/math], 250[math]^\circ[/math], 360[math]^\circ[/math]

Number of Rotational Symmetries

Does a [b]REGULAR Hexagon [/b]have 90° rotational symmetry?

Yes No

List Rotational Symmetries

Choose the list that includes all Rotational Symmetries for a [b]REGULAR Hexagon. [b](Angles at which it lines up with the original pentagon)[/b][/b]

60[math]^{\circ}[/math],120[math]^{\circ}\circ[/math], 180[math]^\circ[/math], 240[math]^\circ[/math], 300[math]^\circ[/math], 360[math]^\circ[/math] 72[math]^\circ[/math], 140[math]^\circ[/math], 216[math]^\circ[/math], 288[math]^\circ[/math], 360[math]^\circ[/math] 80[math]^\circ[/math], 180[math]^\circ[/math], 240[math]^\circ[/math], 360[math]^\circ[/math][br] 60[math]^\circ[/math], 120[math]^\circ[/math], 180[math]^\circ[/math], 360[math]^\circ[/math]

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?

Number of Rotational Symmetries

How many times did the trapezoid land onto itself?

Number of Rotational Symmetries

Does a [b]REGULAR OCTAGON[/b] have 90° rotational symmetry?

Yes No

List Rotational Symmetries

Choose the list that includes all Rotational Symmetries for a[b] Regular Octagon.[/b]

[math]80^\circ,140^\circ,180^\circ,240^\circ,280^\circ,360^\circ[/math] 60[math]^\circ[/math], 120[math]^\circ[/math], 180[math]^\circ[/math], 360[math]^\circ[/math] 45[math]^\circ[/math], 90 [math]^{\circ}[/math], 135[math]^\circ[/math], 180[math]^\circ[/math], 225[math]^\circ[/math], 270[math]^\circ[/math], 315[math]^\circ[/math], 360[math]^\circ[/math] 120[math]^\circ[/math], 240[math]^\circ[/math], 360[math]^\circ[/math][br]

How many sides do the shapes with 90 degree rotational symmetry have? Do you think there's a pattern?

Rotational Symmetry of Regular Polygons

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

Equilateral Triangle

Number of Rotational Symmetries

List Rotational Symmetries

Square

Number of Rotational Symmetries

List Rotational Symmetries

Number of Rotational Symmetries

List Rotational Symmetries

Number of Rotational Symmetries

List Rotational Symmetries

Rotational symmetry of Non-regular polygons

Rectangle (non-regular polygon)

Number of Rotational Symmetries

Number of Rotational Symmetries

Number of Rotational Symmetries

List Rotational Symmetries

Information: Rotational Symmetry of Regular Polygons