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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 30° Angle

(This demonstration shows how to construct a 30° 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|. Label the point where it crosses |PQ| as point B.
  4. Without changing the compass width, move the compass to the point S. Draw a circle that crosses the first one and goes well to the right. Label the point where the two circles cross as point E.
  5. Without changing the compass width, move the compass to the point E, and draw an arc across the previous arc, creating point C.
  6. Draw a line from A to C.
  7. Done. The angle (DAC) has a measure of 30°

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