Benchmark 24 I can use properties of perpendicular bisectors and angle bisectors to identify equal distances.

Perpendicular Bisector Theorem If a point is on the perpendicular bisector of a segment, then the point is __________ from the endpoints of the segment. equidistant

Given: n is the  bisector of AB Prove: For any pt. P on n, PA=PB C B A P StatementsReasons 1.Line n is the  bisector of AB 1. Given 2. AC  BC,2. Def. of  bisector n 3. <ACP and <BCP are rt. <‘s 4. <ACP  <BCP 3. Def. of  4. All rt. <‘s are 

Given: n is the  bisector of AB Prove: For any pt. P on n, PA=PB C B A P StatementsReasons 5. PC  PC 5. Reflexive 6. ΔACP  ΔBCP 6. SAS Post. 7. PA  PB 7. CPCTC 8. PA = PB 8. Def. of  segments n

If a point is equidistant from the _________ of a segment, then it is on the perpendicular bisector the segment. Converse of the Perpendicular Bisector Theorem endpoints

Angle Bisector Theorem If a point is on the bisector of an angle, then the point is __________ from the two sides of the angle. equidistant

Converse Angle Bisector Theorem If a point is on the ______ of an angle and is _________ from the sides of the angle, then it lies on the angle _______. equidistant interior bisector