Construct an Angle Bisector

Constructing an Angle Bisector

An angle bisector is a ray, line, or segment that divides an angle into two equal angles. The key idea is to use a compass and straightedge to create points that are the same distance from the sides of the angle.

Method

1. Start with the given angle. Identify the vertex and the two sides of the angle.
2. Draw an arc from the vertex. With the compass centered at the vertex, draw an arc that crosses both sides of the angle.
3. Mark two intersection points. Label where the arc meets each side.
4. Draw equal-radius arcs. Without changing the compass width, place the compass on each intersection point and draw arcs inside the angle so they intersect.
5. Draw the bisector. Use a straightedge to draw a ray from the vertex through the intersection point of the two inner arcs.

Check

The new ray should split the original angle into two congruent angles. If measuring is allowed, both parts should have the same measure. If not, the construction is correct when the arcs are drawn with the same compass width and the final ray passes through the intersection of the inner arcs.

Common mistake to avoid

Do not change the compass width after the first arc unless the construction specifically requires it. Equal widths are what ensure the two angles are equal.