How to Bisect an Angle Step-by-Step in Geometry

• A straightedge or ruler.
• A compass.
• A pencil.

Examples

Practice Questions:

1. After bisecting \( \angle XYZ \), if \( \angle XYW = 40^\circ \), what’s the measure of \( \angle WYZ \)?
2. Why is angle bisector important in the construction of the incenter of a triangle?
3. If you bisect a right angle, what type of angles do you get?

1. Since \( \angle XYW \) is half of \( \angle XYZ \), \( \angle WYZ \) will also measure \(40^\circ\).
2. The incenter of a triangle is the point where the angle bisectors of the triangle intersect. It’s equidistant from all the triangle’s sides. This equidistance property is crucial for inscribing a circle inside the triangle, known as the incircle.
3. You get two acute angles, each measuring \(45^\circ\).

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