Constructing an Angle Bisector | Step-by-Step Guide with Geometric Tools

definition of angle bisector

An angle bisector is a line or segment that divides an angle into two congruent (equal) angles

An angle bisector is a line or segment that divides an angle into two congruent (equal) angles. In other words, it is a line that splits an angle into two smaller angles that have the same measure. The angle bisector divides the initial angle into two smaller angles, often referred to as the “bisected angles.”

To construct an angle bisector, you can use various geometric tools, such as a compass and a straightedge. Here’s a step-by-step procedure to construct an angle bisector:

1. Draw the given angle using a straightedge. Let’s call the vertex of the angle “V” and the two sides of the angle “a” and “b.”

2. Place the tip of the compass at the vertex “V” and draw an arc that intersects both sides of the angle “a” and “b.” Let the two points of intersection be labeled as “A” and “B” respectively.

3. Without changing the compass’s width, place the compass tip at point “A” and draw an arc that intersects the side “a.”

4. Now, with the compass width still the same, place the compass tip at point “B” and draw another arc that intersects the side “b.”

5. Using a straightedge, draw a line that connects the point of intersection between the arcs on side “a” and “b” to the vertex “V” of the angle. This line is the angle bisector.

The angle bisector is a crucial concept in geometry and often utilized in various geometric proofs and constructions. It helps establish equal measures between angles and allows for the exploration of relationships between angles within shapes or systems.

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