1. Chapter 5 Properties of TrianglesPerpendicular and Angle BisectorsSec 5.1 Goal: To use properties of perpendicular bisectors and angle bisectors

2. Perpendicular Bisector Perpendicular Bisector – a segment, ray, line, or plane that is perpendicular to a segment at its midpoint.

3. Equidistant Equidistant from two points means that the distance from each point is the same.

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

5. Converse of the Perpendicular Bisector Theorem 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 a segment.

6. Example Does D lie on the perpendicular bisector of

7. Example

8. Distance from a point to a line The distance from a point to a line is defined to be the shortest distance from the point to the line. This distance is the length of the perpendicular segment.

9. Angle Bisector Theorem Angle Bisector Theorem – If a point (D) is on the bisector of an angle, then it is equidistant from the two sides of the angle.

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

11. Examples Does the information given in the diagram allow you to conclude that C is on the perpendicular bisector of AB?

12. Examples Does the information given in the diagram allow you to conclude that P is on the angle bisector of angle A?

13. Examples Draw the segment that represents the distance indicated. R perpendicular to LM T perpendicular to AP

14. Examples Name the segment whose length represents the distance between: M to AT T to HM H to MT