5.2 Perpendicular and Angle Bisectors

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

5.2 Perpendicular and Angle Bisectors

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