Question

When constructing an angle bisector, why must the arcs intersect?

Answer 1

The correct answer is:

The arcs must intersect in order to connect to the vertex of the angle.

Explanation:

When constructing an angle bisector, we open our compass to any width, and place the point of the compass on the vertex of the angle. We then construct an arc through both sides of the angle.

Next we move the compass to the point where our constructed arc intersects one side of the angle. We then draw an arc inside of the angle.

Using the compass set to the same width, we move the compass to the point where our first arc intersects the other side of the angle, drawing an arc inside of the angle. This new arc will intersect our previous arc, creating a point.

We then use a straightedge to connect this point to the vertex of the angle, giving us our bisector.

If the two arcs did not intersect, we would not have a point to connect to the vertex.

Answer 2

The arcs have to intersect to give a point which will connect to the vertex of the angle that you are bisecting.