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##### 5.2 Perpendicular and Angle Bisectors

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**5.2 Perpendicular and Angle Bisectors**Objective: I will use properties of perpendicular and angle bisectors**Vocab**1. equidistant: a point that is the same distance from two objects 2. Distance from a point to a line: length of the perpendicular segment from the point on the line**Theorem 5-2: Perpendicular Bisector Theorem**If a point in on the perpendicular bisector of a segment, then it is equidistant from the endpoints of the segment If: Then: PM I AB and MA = MBPA = PB P P B A M B A M**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 If: Then: PA = PB PM I AB and MA = MB P P B A M B A M**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 If: Then: QS bisects <PQR, SP I QP, SP = SR And SR I QR P P Q S Q S R R**Theorem 5-5: Converse of the Angle 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 If: Then: SP = SR, SP I QP,QS bisects <PQR and SR I QR P P Q S Q S R R