|
Bisecting an Angle
Click here for a printable angle bisection worksheet
This demonstration shows how to bisect an angle using
only a compass and straight edge. See " Introduction to Euclidean Constructions"
We start with two lines forming an angle ∠PQR.
The result is a line which exactly bisects the angle - dividing it into two angles of equal measure.
Instructions Click on 'Next' to go through the construction one step at a time, or click on 'Run' to let it run without stopping.
(If there is no image below, see support page.)
The animated diagram above shows how to construct an
angle bisector using just a compass and straightedge.
Note that the straight edge can be a ruler, but it is not used to actually measure anything, just to draw straight lines.
Step-by-step Instructions
| Step 1 |
Place the compass point on the angle's vertex Q. |
| Step 2 |
Adjust the compass to a medium wide setting. The exact width is not important. |
| Step 3 |
Without changing the compass width, draw an arc across each leg of the angle. |
| Step 4 |
The compass width can be changed here if desired. Recommended: leave it the same. |
| Step 5 |
Place the compass on the point where one arc crosses a leg and draw an arc in the
interior of the angle. |
| Step 6 |
Without changing the compass setting repeat for the other leg so that the two arcs cross. |
| Step 7 |
Using a straightedge, draw a line from the vertex to the point where the arcs cross |
| Step 8 |
Done. This is the bisector of the angle ∠PQR. |
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.
Other constructions
Lines
Angles
Triangles
Triangle Centers
Circles, Arcs and Ellipses
Non-Euclidean constructions
(C) 2007 Copyright John Page
|