Angle bisector
a ray that divides an angle into two congruent angles
An angle bisector is a line, ray, or segment that divides an angle into two congruent parts or angles. The point where the angle bisector intersects the angle is called the vertex of the angle.
In a triangle, the angle bisector of an angle intersects the opposite side of the triangle at a point that divides the length of that side in proportion to the lengths of the other two sides. This is known as the Angle Bisector Theorem.
The length of the angle bisector can be calculated using the formula:
Length of angle bisector = (2ab/(a+b)) * cos(theta/2)
where a and b are the lengths of the sides adjacent to the angle being bisected, and theta is the measure of the angle.
There are many applications of the angle bisector in geometry and trigonometry, such as finding the circumcenter and incenter of a triangle, or solving trigonometric equations using angle bisector identities. It is an important concept in Euclidean geometry and has numerous real-world applications, such as in surveying, navigation, and engineering.
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