5.2 Bisectors in Triangles

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## 5.2 Bisectors in Triangles

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**5.2 Bisectors in Triangles**Chapter 5 Relationships Within Triangles**5.2 Bisectors in Triangles**• Theorem 5-2 Perpendicular Bisector Theorem If a point is on the perpendicular bisector of a segment, then it is equidistant from the endpoints of the segment. • Theorem 5-3 Converse of the Perpendicular Bisector Theorem If a point is equidistant from the endpoints of a segment, then it is on the perpendicular bisector of the segment.**5.2 Bisectors in Triangles**C A D B AC = BC, so C is equidistant from the endpoints, and is on the perpendicular bisector**5.2 Bisectors in Triangles**• Theorem 5-4 Angle Bisector Theorem If a point is on the bisector of an angle, then the point is equidistant from the sides of the angle. • Theorem 5-5 Converse of the Angles Bisector Theorem If a point in the interior of an angle is equidistant from the sides of the angle, then the point is on the angle bisector**5.2 Bisectors in Triangles**• Point D is equidistant from the sides of the angle. • Distance is always perpendicular. C D A B**5.2 Bisectors in Triangles**• Find the value of x, then find FD and FB. C B D 5x 2x + 24 F**Practice**• pg 252 12-26