Angle Bisector Construction

Grade 4

What the angle bisector does

The angle bisector cuts an angle exactly in half. Every point on the angle bisector is equidistant from the two arms of the angle. That is the locus property you need to quote in exam questions.

Construction steps

1. Place the compass point at the vertex of the angle and draw an arc that crosses both arms.

2. Place the compass point on each of the two crossing points in turn and draw two arcs that intersect inside the angle. Keep the same compass width for both.

3. Draw a straight line from the vertex through the point where the two arcs meet. This is the angle bisector.

Again, leave all arcs visible. Two crossing arcs inside the angle with a line through them scores full marks — rubbing them out loses you marks.

Worked example

EXAMPLE

A garden has two straight fences meeting at a corner. A path is to be built so it is always equidistant from both fences. Describe the path.

The path must be equidistant from both fence lines. That locus is the angle bisector of the angle formed by the fences. Construct the bisector of the angle at the corner — the path follows the angle bisector of the angle between the two fences.

Try this one

A point \( P \) moves so that it is always exactly \( 4 \) cm from a fixed point \( O \).

Describe fully the locus of the point \( P \). [2]

Nova's hint:

This is about the locus of points a fixed distance from a single point.

Ask yourself: 'if I stay the same distance from one point in every direction, what shape do I trace out?' Think about what all those points have in common.

Try to Solve it with Nova?