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Constructing a 60° angle
Geometry construction using a compass and straightedge
| After doing this |
Your work should look like this |
| 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 PQ. P will be the angle's vertex. |
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| 2. Set the compass on P, and set its width to any convenient setting. |
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| 3. Draw an arc across PQ and up over above the point P. |
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| 4. Without changing the compass width, move the compass to the point where the arc crosses PQ, and make an arc that crosses the first one. |
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| 5. Draw a line from P, through the intersection of the two arcs. |
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| 6. Done. The angle QPR has a measure of 60° |
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Proof
This construction works by creating an
equilateral triangle.
Recall that an equilateral triangle has all three interior angles 60°.
The image below is the final drawing above with the red items added.
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Argument |
Reason |
| 1 |
Line segments AB, PB, PA are
congruent |
All drawn with the same compass width. |
| 2 |
Triangle APB is an
equilateral triangle |
Equilateral triangles are those with all three sides the same length. |
| 3 |
Angle APB has a measure of 60° |
All three interior angles of an equilateral triangle have a measure of 60°.
See Equilateral triangle definition |
- Q.E.D
Try it yourself
Click here for a printable worksheet containing two 60° angle exercises.
When you get to the page, use the browser print command to print as many as you wish. The printed output is not copyright.
Constructions pages on this site
Lines
Angles
Triangles
Triangle Centers
Circles, Arcs and Ellipses
Polygons
Non-Euclidean constructions
(C) 2009 Copyright John Page
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