Angle Bisector
An angle bisector is a geometric line or line segment that divides an angle into two equal parts
An angle bisector is a geometric line or line segment that divides an angle into two equal parts. In other words, it splits the angle into two congruent (equal) angles. The angle bisector intersects the angle at its vertex, dividing it into two smaller angles that have the same measure.
To construct an angle bisector, you can use a compass and ruler. Here’s how you can do it:
1. Draw the angle: Start by drawing the two rays that form the angle. Ensure that the rays intersect at a common point, which is the vertex of the angle.
2. Place the compass on the vertex: Open the compass to a convenient width and place its pointed end on the vertex of the angle.
3. Draw two arcs: While keeping the compass at the same width, draw arcs intersecting each ray of the angle.
4. Connect the two points of intersection: Use a ruler to draw a straight line connecting the two points where the arcs intersect the rays.
The line segment you just drew is the angle bisector. It divides the original angle into two equal parts.
Angle bisectors have several properties that are useful in geometry, such as:
1. Angle Bisector Theorem: If a line segment divides an angle into two congruent angles, then it divides the opposite side of the angle into two segments that are proportional to the adjacent sides of the angle.
2. Interior and Exterior Angles: The angle bisector of an interior angle of a triangle is always inside the triangle, while the angle bisector of an exterior angle is always outside the triangle.
3. Angle Bisector in Circles: The angle bisector of an angle formed by two chords of a circle passes through the center of the circle.
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