Angle Bisector Theorem
The Angle Bisector Theorem states that within a triangle, when an angle bisector is drawn from a vertex and it extends to one side, this bisector divides that side in a proportion equivalent to the ratio of the other two sides of the triangle, it means that the relationship between the segments formed by the angle bisector on one side is directly linked to the relative lengths of the other two sides of the triangle.
Interior Angle Bisector Theorem
The Interior Angle Bisector Theorem states that the interior angle bisector of a triangle joining the opposite side divide the opposite sides in proportion to the remaining two sides of the triangle.
External Angle Bisector Theorem
External Angler Bisector Theorem states that the bisector of exterior angle of a triangle divides the opposite side externally in the ratio equal to the ratio of the sides enclosing the angle.
Angle Bisector Theorem Formula
The triangle angle bisector theorem states that in a triangle, the bisector of any angle divides the opposite side into segments that are proportional to the other two sides of the triangle.
Mathematically, let’s say we have a triangle ABC, with angle bisector AD, where D is on side BC. The theorem can be expressed as:
BD/DC = AB/AC
Angle Bisector
Angle Bisector in geometry is a line, ray, or segment that divides an angle into two equal angles of the same measure. The word Bisector means dividing a shape or an object into two equal parts. In the case of geometry, it is often used to split triangles and angles into equal measures.
In this article, we will discuss the introduction, definition, and properties of an Angle Bisector and its meaning. We will also understand the construction of an Angle Bisector and the theorem to calculate the angle. We will also solve various examples and provide practice questions for a better understanding of the concept of this article.
Table of Content
- What is an Angle Bisector?
- Angle Bisector of Triangle
- Properties of Angle Bisector
- Construction of an Angle Bisector
- Angle Bisector Theorem
- Perpendicular Bisector Theorem
- Solved Example of Angle Bisector
- Practice Questions on Angle Bisector