1. 5.2: Bisectors in Triangles Objectives: To use properties of perpendicular and angle bisectors

2. Warm Up 1.What is a perpendicular bisector of a segment? 2.What is an angle bisector? 3.What does equidistant mean?

3. is the perpendicular bisector of What do we know?

4. 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 Perpendicular Bisector Theorem If a point is equidistant from the endpoints of a segment, then it is on the perpendicular bisector of the segment. 6 6 IS THE PERPENDICULAR BISECTOR OF SEGMENT AB

6. EXAMPLES 1.Find PB and AQ. 14 7

7. Find AD, x, and BC. C D A B 12 2x+6 3x+1

8. What do we know about P? 10

9. Definition The distance from a point to a line is defined as the length of the perpendicular segment from the point to the line.

10. Angle Bisector Theorem If a point is on the bisector of an angle, then the point is equidistant from the sides of the angle. 4 4

11. Converse of 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.

12. Let’s try an example… Solve for x. Then find AD & CD. 5x 2x + 24 5x = 2x + 24 3x = 24 X = 8 AD=5*8=40 CD=2*8+24= 40