An angle bisector is a ray that originates from the vertex of an angle and divides it into two smaller, equal angles.
Every point on an angle bisector is equidistant from the two rays (arms) that form the original angle.
To construct it, draw an arc centered at the vertex to mark equal distances on both arms, then draw two intersecting arcs from those marks into the center of the angle.
Connecting the vertex to the intersection of these two arcs creates the bisecting line, effectively splitting the angular space in half.
It is vital to distinguish between constructions based on points versus those based on lines to solve locus problems correctly.
| Feature | Perpendicular Bisector | Angle Bisector |
|---|---|---|
| Purpose | Equidistant from two points | Equidistant from two lines |
| Starting Input | A line segment | An angle (two intersecting lines) |
| Geometric Result | A line at to the segment | A ray splitting the angle |
| Key Tool Use | Arcs from segment endpoints | Arcs from vertex and arm marks |
Keep Construction Lines: Never rub out your arcs. Examiners use these to verify that you followed the correct geometric procedure rather than just guessing.
Pencil Precision: Use a very sharp pencil (preferably 2H or H) to ensure lines are thin and intersections are clear; a blunt pencil can lead to errors of 1-2 mm, which may lose marks.
Compass Tension: Ensure your compass hinge is tight so the width does not slip while drawing arcs, as this is the most common cause of inaccurate constructions.
Verification: After constructing, use a ruler or protractor to check your work. For example, measure both halves of a bisected angle to ensure they are equal.
