Constructing An Angle Bisector: Step-By-Step Guide With Compass And Straightedge

angle bisector

a ray that divides an angle into two equal angles

In geometry, an angle bisector is a line, ray or line segment that divides an angle into two equal parts. This means that the angle bisector splits the angle into two congruent angles.

To construct an angle bisector, you need a compass and a straightedge. Here are the steps to construct an angle bisector:

1. Draw the angle: Start by drawing the two sides of the angle using a straightedge.

2. Place the compass at the vertex: Place the tip of the compass at the vertex of the angle.

3. Draw an arc: Use the compass to draw an arc that intersects both sides of the angle.

4. Repeat on the other side: Without changing the compass width, place the compass tip at the other side of the angle and draw another arc that intersects the first arc.

5. Draw the bisector: Use a straightedge to draw a line connecting the vertex to the point where the two arcs intersect.

This line is the angle bisector and it divides the angle into two equal parts.

Angle bisectors have many applications in geometry, including finding the center of a circle inscribed in a triangle, proving theorems and solving problems involving angles.

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