Angle Bisector
A line through the vertex of an angle that divides it into two equal angles.
An angle bisector is a line or ray that divides an angle into two equal parts. It starts from the vertex of the angle and passes through the angle to the opposite side. The point where the angle bisector intersects with the opposite side is called the point of intersection or the foot of the angle bisector. The theorem that governs angle bisectors is called the angle bisector theorem which states that an angle bisector divides the opposite side into two segments that are proportional to the adjacent sides of the angle.
In trigonometry, the angle bisector divides the opposite side into two segments, a and b, where a/b = c/d, where c and d are the adjacent sides of the angle. This theorem is useful in solving trigonometric problems involving angles and sides of a triangle.
The angle bisector is also used in constructing geometric figures. For example, to construct an equilateral triangle, we can start with any point as the vertex and draw an angle bisector. Then we can draw circles centered at the vertex passing through the point of intersection of the angle bisector and the opposite side. The points where the circles intersect with the two sides of the angle form the other two vertices of the equilateral triangle.
In summary, an angle bisector is a line or ray that divides an angle into two equal parts. It is governed by the angle bisector theorem and is used in solving trigonometric problems and constructing geometric figures.
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