Bisecting an Angle
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