How do you divide an angle in half using compass?

Answer 1

This browser is useless for graphics so the answer will be a bit clumsy:

1. Place the point of the compass at O, the vertex of the angle, and draw an arc that intersects the two arms of the angle at points A and B.

2. Place the point of the compass at A. Make sure that the radius of the compass is greater than half the distance from A to the other arm of the angle. Draw an arc, inside the angle and in the direction away from O.

3. Move the point of the compass to B without changingthe radius and draw another arc so that it intersects the last arc at C.

4. Join OC. It divides the angle in half.

You cannot because, in addition to a compass, you will also need a straight edge.

Answering this question is not going to be easy with a browser that cannot handle even the simplest graphics, but I will try. It is probably best if you follow these steps using paper and pencil.

Suppose you have rays XO and YO that meet at O and you wish to bisect angle XOY. Put the compass point at O and with any convenient radius draw an arc that intersects XO at P and YO at Q.

Now put the compass point at P and draw an arc inside angle XOY, using a radius that is at least a little more than half the distance between P and Q. Using the same radius, draw an arc with the compass point at Q so that these two arcs intersect at R. The the straight line OR, drawn using the straight edge, will bisect the angle XOY, as required.

Answer 2

This browser is useless for graphics so the answer will be a bit clumsy:

1. Place the point of the compass at O, the vertex of the angle, and draw an arc that intersects the two arms of the angle at points A and B.

2. Place the point of the compass at A. Make sure that the radius of the compass is greater than half the distance from A to the other arm of the angle. Draw an arc, inside the angle and in the direction away from O.

3. Move the point of the compass to B without changingthe radius and draw another arc so that it intersects the last arc at C.

4. Join OC. It divides the angle in half.

Answer 3

You cannot because, in addition to a compass, you will also need a straight edge.

Answering this question is not going to be easy with a browser that cannot handle even the simplest graphics, but I will try. It is probably best if you follow these steps using paper and pencil.

Suppose you have rays XO and YO that meet at O and you wish to bisect angle XOY. Put the compass point at O and with any convenient radius draw an arc that intersects XO at P and YO at Q.

Now put the compass point at P and draw an arc inside angle XOY, using a radius that is at least a little more than half the distance between P and Q. Using the same radius, draw an arc with the compass point at Q so that these two arcs intersect at R. The the straight line OR, drawn using the straight edge, will bisect the angle XOY, as required.