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5.2 Bisectors of Triangles

5.2 Bisectors of Triangles. Use the properties of perpendicular bisectors of a triangle Use the properties of angle bisectors of a triangle. A perpendicular bisector of a triangle is a line (or ray or segment) that is perpendicular to the side of a triangle at the midpoint of the side

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5.2 Bisectors of Triangles

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  1. 5.2 Bisectors of Triangles • Use the properties of perpendicular bisectors of a triangle • Use the properties of angle bisectors of a triangle

  2. A perpendicular bisector of a triangle is a line (or ray or segment) that is perpendicular to the side of a triangle at the midpoint of the side Concurrent linesare 3 or more lines (rays or segments) that intersect at the same point The Point of concurrency is the point of intersection. Definitions

  3. In a triangle, the Point of Concurrency is called the Circumcenter of the triangle • The circumcenter can be located inside, on or outside the triangle. • It is called the circumcenter because it is the center of a circle that passes through all the vertices of the triangle

  4. Theorem 5.5 - Concurrency of Perpendicular Bisectors of a Triangle • The Perpendicular Bisectors of a triangle intersect at a point that is equidistant from the vertices of a triangle. (PA = PB = PC)

  5. Definitions • An Angle Bisector of a Triangle is a bisector of an angle of a triangle • The Incenter of the Triangle is the point of concurrency of the angle bisectors • The Incenter always lies inside the triangle.

  6. Theorem 5.6 (Concurrency of Angle Bisectors of a Triangle): • The angle bisectors of a triangle intersect at a point that is equidistant from the sides of the triangle.

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