How to Construct a Regular Pentagon With a Compass and Straightedge

A pentagon's sides are of equal length.

Pentagons are five-sided polygons with an interior angle of 72 degrees on each corner. While the easiest way to draw a pentagon is to use a protractor to find the corner angles, you can also construct one using a compass and ruler. You will contruct the pentagon within a circle drawn with the compass.

Things You'll Need

• Pencil
• Ruler
• Compass

Instructions

1. Draw two straight lines on a piece of paper, crossing each other at 90 degrees, with equal lengths either side of the intersection.

2. Position the anchor point of the compass on the intersection. Draw a circle around this point.

3. Draw a straight line (T1) in the top-right section, level with the edge of the circle and running parallel to the main horizontal line (H1). Draw another straight line (T2) in this section, parallel to the main vertical line (V1). Ensure that you make the lines long enough for them to cross.

4. Draw a line diagonally from the center intersection to the intersection of H1 and V1. Draw another diagonal line that crosses this from the edge of the circle on V1 to the edge of the circle on H1. Draw a vertical line (V2) through the new intersection, parallel to V1.

5. Measure the distance between the edge of the circle on V1 to the point where V2 meets H1. Set the compass to this distance.

6. Position the compass anchor point on the intersection between H1 and V2. Draw an arc between the point where the edge of the circle crosses V1 to H1 in the top-left segment. Measure the length between the two points and set the compass to this distance.

7. Position the compass anchor point on the point where the edge of the circle crosses V1. Draw an arc in the circle that crosses the edge of the circle on opposite sides. Position the compass anchor point on each of the new intersections. Draw arcs in the circle that cross the edge of the circle on opposite sides.

8. Draw straight lines between the points where the arcs cross the edge of the circle to construct your pentagon.

References

• Beth Lee Design: Construct a Pentagon or Decagon