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Section 5-2. Bisectors of a Triangle. Perpendicular bisector of a triangle. A line, ray, or segment that is perpendicular to a side of the triangle at the midpoint of the side. Perpendicular Bisector. Concurrent lines. When three or mores lines (rays or segments) intersect in the same point.
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Section 5-2 Bisectors of a Triangle
Perpendicular bisector of a triangle • A line, ray, or segment that is perpendicular to a side of the triangle at the midpoint of the side.
Concurrent lines • When three or mores lines (rays or segments) intersect in the same point Point of concurrentcy • The point of the intersection of the lines
The three perpendicular bisectors of a triangle are concurrent!
The point of concurrency: • Is inside an acute triangle
Circumcenter of a triangle • The point of concurrency of the perpendicular bisectors of the triangle.
Concurrency of perpendicular bisectors of a triangle theorem • The perpendicular bisectors of a triangle intersect at a point that is equidistant from the vertices of the triangle
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ANGLE BISECTOR OF A TRIANGLE • A bisector of an angle of a triangle
Incenter of the triangle • The point of concurrency of the angle bisectors • Always lies inside the triangle!
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Concurrency of angle bisectors of a triangle theorem • The angle bisectors of a triangle intersect at a point that is equidistant from the sides of the triangle.
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