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Bisecting an Angle
Geometry construction using a compass and straightedge
How to bisect an angle with compass and straightedge or ruler. To
bisect an angle means that we divide the angle into two equal
(congruent)
parts without actually measuring the angle. This Euclidean construction works by creating two
congruent triangles.
See the proof below for more on this.
| After doing this |
Your work should look like this |
| Start with angle PQR that we will bisect. |
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| 1. Place the compass point on the angle's vertex Q. |
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| 2. Adjust the compass to a medium wide setting. The exact width is not important. |
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| 3. Without changing the compass width, draw an arc across each leg of the angle. |
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| 4. The compass width can be changed here if desired. Recommended: leave it the same. |
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| 5. Place the compass on the point where one arc crosses a leg and draw an arc in the
interior of the angle. |
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| 6. Without changing the compass setting repeat for the other leg so that the two arcs cross. |
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| 7. Using a straightedge or ruler, draw a line from the vertex to the point where the arcs cross |
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| Done. This is the bisector of the angle ∠PQR. |
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Proof
This construction works by effectively building two congruent triangles.
The image below is the final drawing above with the red lines added and points A,B,C labelled.
- Q.E.D
Try it yourself
Click here for a printable worksheet containing three angle bisection problems.
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
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