1. 1.5 Segment and Angle Bisectors
Geometry
1.5 Segment and Angle Bisectors

2. Bisecting a Segment
The midpoint of a segment is the point that divides, or bisects (divide into two equal parts), the segment into two congruent segments.
A segment bisector is a segment, ray, line, or plane that intersects a segment or its midpoint

3. Finding the Midpoint
If you know the coordinates of the endpoints of a segment, you can calculate the coordinates of the midpoint. You simply take the mean, or average, of the x-coordinates and of the y-coordinates. This method is summarized as the Midpoint Formula

4. Midpoint Formula

5. Find the Midpoint Graph the points A(-2, 3) and B(5, -2)
Use the Midpoint Formula to find the coordinates of the midpoint of segment AB.

6. Find the Midpoint Graph the points D(3, 5) and E(-4, 0)
Use the Midpoint Formula to find the coordinates of the midpoint of segment DE.

7. Find the Other Endpoint of a Segment
Graph the points X(-3, 1) and M(3, -4)
The midpoint of segment XY is M. One endpoint is X. Find the coordinates of the other endpoint.

8. Find the Other Endpoint of a Segment
Graph the points R(-1, 7) and M(2, 4)
The midpoint of segment RP is M. One endpoint is R. Find the coordinates of the other endpoint.

9. Bisecting an Angle
An angle bisector is a ray that divides an angle into two adjacent angles that are congruent.

10. The ray FH bisects the angle EFG
The ray FH bisects the angle EFG. Given that the measure of angle EFG = 120 degrees, what are the measures of angle EFH and angle HFG?
Example 1

11. Example 2
Angle CBA is bisected by ray BD. The measure of angle DBA is 65 degrees. Find the measure of angle CBA.

12. Example 3
In the diagram, ray RQ bisects angle PRS. The measures of the two congruent angles are (x+40) degrees and (3x – 20) degrees. Solve for x.
(x + 40)
(3x – 20)