angle bisector of a triangle
A segment that bisects an angle of the triangle and has one endpoint at a vertex of the triangle and the other endpoint on the opposite side of the triangle.
The angle bisector of a triangle is a line or a ray which divides one of the angles of the triangle into two equal parts. Therefore, it is a line or a ray that starts at one of the vertices of the triangle and passes through the opposite side of the triangle, dividing the angle into two equal parts. Every triangle has three angle bisectors, one for each of its angles.
To construct the angle bisector of a triangle, you need to follow these steps:
1. Draw your triangle on a piece of paper
2. Choose one of the angles of the triangle that you want to bisect
3. Draw a ray that starts at the vertex of the angle you chose
4. Divide the angle into two equal parts using a protractor or compass
5. Draw a line that goes through the point where the ray meets the opposite side of the triangle and is perpendicular to that side
6. Repeat this process for the other two angles of the triangle
The angle bisectors of a triangle have several important properties. For example, the three angle bisectors of a triangle always intersect at the incenter of the triangle. Additionally, the incenter of a triangle is equidistant from the sides of the triangle. This means that if you draw a circle with the incenter as its center and the length of the radius equal to the distance from the incenter to one of the sides of the triangle, that circle will be tangent to all three sides of the triangle. The angle bisectors also divide the opposite sides of the triangle into segments that are proportional to the adjacent sides.
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The Perpendicular Bisectors Of A Triangle: Properties, Use In Circumcenter And Congruence.