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Section 5-2

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

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  1. Section 5-2 Bisectors of a Triangle

  2. 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.

  3. Perpendicular Bisector

  4. 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

  5. The three perpendicular bisectors of a triangle are concurrent!

  6. The point of concurrency: • Is inside an acute triangle

  7. Is on a right triangle

  8. Is outside an obtuse triangle

  9. Circumcenter of a triangle • The point of concurrency of the perpendicular bisectors of the triangle.

  10. 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

  11. B P A C

  12. ANGLE BISECTOR OF A TRIANGLE • A bisector of an angle of a triangle

  13. Incenter of the triangle • The point of concurrency of the angle bisectors • Always lies inside the triangle!

  14. B A C P

  15. 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.

  16. B D F A C E P

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