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Copying a Line Segment
Constructing a 30° Angle
Constructing a 60° Angle
Finding the Center of a Circle
Constructing Circumcenter of a Triangle
Constructing an Equilateral Triangle
Constructing a Perpendicular Bisector of a Line Segment
Constructing a Perpendicular at the Endpoint of a Ray
Constructing Tangents Through an External Point

Constructing a 60° Angle

(This demonstration shows how to construct a 60° angle from scratch using a compass and straightedge)

Step by Step Instructions
  1. Draw a line segment which will become one side of the angle (Skip this step if you are given this line). The exact length is not important. Label it |AD|. A will be the angle's vertex.
  2. Set the compass on A, and set its width to any convenient setting.
  3. Draw a circle across |AD| and up over above the point A.
  4. Without changing the compass width, move the compass to the point where the circle crosses |AD|, and make a circle that crosses the first one.
  5. Draw a line from A, through the intersection of the two circles.
  6. Done. The angle (DAB) has a measure of 60°.

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