Construction #3
Bisect an Angle
To see a video of Mr. Ochs doing examples
Mr Ochs Video To see and example done in flash click on a link below Math Open Ref Math is Fun 

Given an angle, construct the angle bisector of the given angle.
Construct the angle bisector of angle ABC
1) Choose any radius for the compass
(remember the larger the radius the better the construction )
2) With this radius place your compass pointer on the vertex of the angle to be bisected, then strike an arc that passes through both sides of the angle to get 2 points of intersection X and Y equidistant from the vertex.
3) Now move the pointer of the compass to one of the points(X or Y) where the arc intersects a side, then with a radius greater than 1/2 XY, strike an arc in the middle of interior of the angle.
(this arc should not be close to the vertex)
4) Keeping the same radius as in step 3, move the pointer to the other point (X or Y) where the arc intersects the 2nd side and strike an arc intersecting the arc from step 3.
5) With a straight edge draw a ray from the vertex through the point of intersection created by the intersection of the arcs in steps 3 and 4.
Construct the angle bisector of angle ABC
1) Choose any radius for the compass
(remember the larger the radius the better the construction )
2) With this radius place your compass pointer on the vertex of the angle to be bisected, then strike an arc that passes through both sides of the angle to get 2 points of intersection X and Y equidistant from the vertex.
3) Now move the pointer of the compass to one of the points(X or Y) where the arc intersects a side, then with a radius greater than 1/2 XY, strike an arc in the middle of interior of the angle.
(this arc should not be close to the vertex)
4) Keeping the same radius as in step 3, move the pointer to the other point (X or Y) where the arc intersects the 2nd side and strike an arc intersecting the arc from step 3.
5) With a straight edge draw a ray from the vertex through the point of intersection created by the intersection of the arcs in steps 3 and 4.