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How to Use a Compass to Draw a Pentagon

Updated February 21, 2017

A pentagon is any five-sided polygon shape. A simple pentagon has five even 108-degree internal angles that add up to total of 540 degrees. There are a few methods of drawing a simple pentagon. One way is to use a protractor to measure the angles for each of the sides. Another complex way involves internal angle measurements. You can also use a simple and accurate method of drawing a pentagon using only a drafting compass and a ruler.

Get a sheet of paper, preferably graphing paper, and prepare the compass. Make sure the compass pencil and pencil are both sharp. It is best that the paper be on a hard, flat surface for more accurate lines.

Draw a perfect circle in the middle of the paper with the compass. The circle should be a minimum of 2 inches across to be easier to work with. Draw a dot at the centre point of the circle and label it "O." Leave a lot of free space around the circle to draw on in the following steps. A one-circle width of space all around the original circle you draw is good.

Obtain the first vertex by using the edge of a ruler to draw a straight, vertical line through either side of the circle so that it passes through point "O." This line passes through the original circle at two points on the top and bottom of the circle; label the top point "A" with a large dot. This is the top corner of the pentagon.

Draw the point "B" by using the edge of a ruler to draw a straight line perpendicular (horizontal) to the line "OA" that passes through centre point "O." This line passes through the original circle at two points on the left and right of the circle; label the right point "B" with a large dot.

Find the midpoint of line "OB." Use a ruler to measure halfway from point "O" to point "B" and label the point "C" with a large dot.

Find the midpoint of the line opposite line segment "OB." Use a compass to draw a circle centred at "C" that passes through point "A." This circle passes through the line segment opposite to line segment "OA"; label this point "D" with a large dot.

Obtain the second and third vertices by using the compass to draw a circle centred at point "A" that passes through point "D." This circle passes through the original circle at two points on the upper left and upper right; label these points as "E" and "F" with a large dot. These are the upper left and right corners of the pentagon.

Obtain the fourth vertex by using the compass to draw a circle centred at point "E" that passes through point "A." This circle passes through the original circle at one point on the bottom left; label this point "G" with a large dot. This is the lower left corner of the pentagon.

Obtain the fifth vertex by drawing a circle with the compass centred at point "F" that passes through point "A." This circle passes through the original circle at one point on the bottom left; label this point "H" with a large dot. This is the lower right corner of the pentagon.

Draw the pentagon. Erase all lines, circles and points except for the five points "A," "E," "G," "H" and "F." Use the edge of a ruler to connect each of these five points of the pentagon.

Tip

Use light lines except for the pentagon vertices because everything else needs to be erased after obtaining the five vertices. Draw each circle in a different colour to help you keep track of what you are doing.

Things You'll Need

• Paper (graphing, if possible)
• Drafting compass with a pencil
• Pencil
• Ruler
• Coloured pencils (optional)