You have learned about rotational symmetry in [url=https://www.geogebra.org/m/chbfzetv]this activity.[br][/url]Now let's use the rotational symmetry of a regular polygon to explore its lines of symmetry.[br][br]The [b][i]lines of symmetry[/i][/b] are straight lines that divide a shape into two equal parts, where one part is an exact reflection of the other.[br][br]Select the number of [i][b][color=#6aa84f]sides[/color][/b][/i] of your polygon, and [i][b][color=#674ea7]rotate[/color][/b][/i] it. [br][br]Every time that the rotated polygon overlaps the original one, press the [b][i]Stamp[/i][/b] button on top right, to get a copy of the displayed line stamped in the app. Complete the full rotation of your polygon.[br][br]You can delete all the lines you stamped by pressing the [b][i]Erase [/i][/b]button displayed below the [b][i]Stamp [/i][/b]one.[br][br]
Consider your polygon and the lines you have stamped. [br][br]Are these lines of symmetry for your polygon?[br]Can you relate the number of lines of symmetry of a regular polygon and the number of its sides?
All regular polygons share the property that the [b][i]number of sides[/i][/b] is [b][i]equal [/i][/b]to the [b][i]number of lines of symmetry[/i][/b].[br][br]Thus for example a regular triangle has 3 lines of symmetry, a regular hexagon has 6 lines of symmetry, and so on.[br][br]
Now consider a circle, and the definition of lines of symmetry.[br][br]How many lines of symmetry does a circle have?[br]
We can split a circle into two congruent semicircles by using a diameter, but we can place diameters anywhere in the circle![br][br]This is why [b][i]a circle has infinitely many lines of symmetry[/i][/b].