Construct a regular triangle, hexagon, square in a circle

Regular Shapes

A regular shape has all sides and all angles the same.

Circles

We use circles to measure distance because the radius is always the same for the circle.

Construct a circle

Create a line segment for your radius. Use the compass tool to generate a circle with a radius of the length of the segment.

Regular Triangle

To construct a regular triangle you need 2 circles with the same radius. Construct a line segment. Use the compass tool to create a circle with a radius of that line segment whose center is on the endpoint. Use the compass tool a second time to create a circle with the same radius that is on the other endpoint. The point of intersection is the same distance (equidistant) from the end points. Use the point tool to place the point of intersection. Use the segment tool to connect the two endpoints and the point of intersection.

Construct a Square

A square has equal length sides. 1) Construct a circle (not compass) 2) Construct a line (not segment) through the center of the circle and a point on the edge of the circle. 3) Use the point tool to find the point of intersection on the circle and the line. 4) Use line segment tool to connect the end points on the circle. 5) Use the perpendicular bisector tool to cut the line segment in half. 6) Use the point tool to mark the points of intersection with the perpendicular bisector and the circle. 7) Use the line segment tool to connect the 4 points on the circle to construct the square.

Construct a Regular Hexagon

A hexagon has 6 sides. A regular hexagon has all sides the same length.

a circle has 360º 360 ÷ 6 = 60º An equilateral triangle has 60º angles. 1)Construct an equilateral triangle (see above) 3) Use the compass tool to construct a circle with the same radius length but the center is the point of intersection for the previous 2 circles. 4) Mark the point of intersection with the previous circle 5) Repeat so that you are going all the way around the original circle. 7) Use the line segment tool to connect the points.