1. Chapter 5.1 Segment and Angle Bisectors
Remember the Distance Formula!!

2. Perpendicular Bisector Theorem
Theorems
Perpendicular Bisector Theorem
If a point lies on the ______________ bisector of a segment, then it is _______________ from the endpoints of the segment.
perpendicular
equidistant

3. Perpendicular Bisector Theorem
=Distance
=Distance
Line segment
endpoint
endpoint

4. Theorems
Converse of Perpendicular Bisector Theorem

5. Converse of Perpendicular Bisector Theorem
=Distance
=Distance
Line segment
endpoint
endpoint

6. Angle Bisector Theorem
Theorems
Angle Bisector Theorem
bisector
If a point lies on the ____________ of an angle, then it is _____________ from both sides of the angle.
equidistant

7. Theorems
Converse of Angle Bisector Theorem

8. Angle Bisector Theorem
=Distance
=Distance
side of <G
side of <G G

9. Distance Formula
MIDPOINT Formula

10. Slope Formula

11. Examples
Graph the line segment then construct a perpendicular bisector.
1. Get a piece of graph paper.
2. Graph the line segment AB .
A ( -2, 5) B ( 4, -3).
3. Find the midpoint and slope of AB . ( slope).
4. Plot the midpoint, and count the slope.
5. Highlight the perpendicular bisector.

12. Examples Construct an angle bisector 1. Draw an angle (of any size)
2. Use a compass and make an arc (from the vertex) that intersects both sides of the angle
3. Mark the points where the arc intersects the sided.
4. Using the same radius (on the compass), make another arc from both points of intersection.
5. Mark the point where these two arcs intersect
6. Draw a line from the arc intersection through the vertex of the angle