Understanding Angle Bisectors | Construction, Theorem, and Applications in Geometry and Trigonometry

definition of angle bisector

An angle bisector is a line or ray that divides an angle into two equal parts

An angle bisector is a line or ray that divides an angle into two equal parts. When an angle is bisected, it creates two smaller angles that have the same measure. The line or ray that bisects the angle passes through the vertex of the angle and divides it into two adjacent angles of equal size.

To construct an angle bisector, you can follow these steps:
1. Draw the angle with a compass and straightedge.
2. Place the compass on the vertex of the angle and draw an arc that intersects both sides of the angle.
3. Without changing the compass width, place the compass on the two points where the arc intersected the sides of the angle, and draw two arcs that intersect each other.
4. Draw a straight line from the vertex of the angle to the point where the two arcs intersect. This line is the angle bisector.

The angle bisector theorem is an important concept related to angle bisectors. It states that if a ray bisects an angle of a triangle, it divides the opposite side of the triangle into two segments that are proportional to the other two sides of the triangle.

Angle bisectors have various applications in geometry and trigonometry. They help determine the relationships between angles and sides of shapes, assist in constructing accurate geometric figures, and are useful in solving problems involving triangles and angles.

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