Mastering the Basics | Understanding Angle Bisectors and Their Applications in Geometry

Angle bisector Chapter 1 (p. 40)

In geometry, an angle bisector is a line or ray that divides an angle into two congruent angles

In geometry, an angle bisector is a line or ray that divides an angle into two congruent angles. It is essentially a line or ray that splits the angle into two equal parts. The point where the angle bisector intersects the angle is called the vertex of the angle.

There are different types of angle bisectors, namely internal angle bisectors and external angle bisectors.

1. Internal Angle Bisector: An internal angle bisector divides an angle into two smaller angles on the inside of the angle. It starts from the vertex and extends outwards, intersecting the opposite side or ray.

2. External Angle Bisector: An external angle bisector also divides an angle into two smaller angles, but it extends outside the angle. It starts from the vertex and extends in the opposite direction, intersecting the opposite side or extension of the side.

The angle bisector theorem is a property that relates the lengths of the sides created by an angle bisector. According to this theorem, if a line or ray bisects an angle of a triangle, then it divides the opposite side into two segments that are proportional to the lengths of the other two sides.

Angle bisectors have various applications in geometry and trigonometry. They can be used to determine unknown angles or to find the point equidistant from two given points. In constructions, angle bisectors are often used to construct various geometric figures with precise angles.

When working with angle bisectors, it is important to remember relevant geometric properties and theorems, such as the Angle Bisector Theorem and the properties of congruent triangles. These concepts are fundamental in solving problems and proving geometric relationships involving angle bisectors.

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