Regular Polygons and Polygrams

[left][img]data:image/png;base64,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[/img] This is the regular polygon tool. Plot two points then enter the number of vertices (4 vertices makes a square, etc). Click [url=https://www.mathsisfun.com/definitions/regular-polygon.html]here[/url] to find out what a 'regular polygon' is.[/left][left][img]data:image/png;base64,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[/img]This is the polygon tool. Click on points. Return to your first point to 'close' the polygon. Click [url=https://www.mathsisfun.com/geometry/polygons.html]here[/url] to find out what a 'polygon' is.[/left]

TASK 1: Pentagon

Use the 'regular polygon' tool to make a copy of the shape shown. [br][br]When you've made your pentagon, use the 'arrow' tool to drag you pentagon over the top of the one shown, to check that it is identical.

Pentagon

TASK 2: Pentagon with 5 point star

Use the 'regular polygon' tool to draw the pentagon.[br][br]Then use the 'polygon' tool to draw the five point star (pentagram). Start at any point, click on every 2nd point.[br][br]You can read about this historically rich shape here: [url=https://www.mathsisfun.com/geometry/pentagram.html]https://www.mathsisfun.com/geometry/pentagram.html[/url]

Pentagon with 5 point star

TASK 3: Hexagon with two equilateral triangles

Make an identical copy of this diagram.[br][br]Use the 'regular polygon' tool to create the hexagon.[br][br]Use the 'polygon' tool or the 'regular polygon' tool to create the two equilateral triangles.

TASK 4: Octagon with two overlapping squares

Make an identical copy of this diagram.[br][br]Use the 'regular polygon' tool to create the octagon.[br][br]Use the 'polygon' tool or the 'regular polygon' tool to create the two overlapping squares.

TASK 5: Octagon with 8 point star, continuous line

Make an identical copy of this diagram.[br][br]Use the 'regular polygon' tool to create the octagon.[br][br]Use the 'polygon' tool to create the continuous line that makes the star. Join every third point.

TASK 6

Make a regular polygon that has 7 sides or more than 8 sides.[br][br]Create a star inside the polygon.

TASK 7

Create a new regular polygon diagram.

Observation(s)

Explain/describe a numerical or spatial pattern you notice about these regular polygon/star diagrams.

Decagram (optional task)

Look up the page [url=https://mathworld.wolfram.com/Polygram.html]https://mathworld.wolfram.com/Polygram.html[/url].[br][br]Describe how to make a 'decagram' below.[br][br]Use the 'task 7' applet (slide the grid over if you already have a diagram there) or, open a geogebra classic page ([url=https://www.geogebra.org/classic]https://www.geogebra.org/classic[/url]). Use the tools provided to construct a decagram.