1. 1.5 Segment & Angle Bisectors

2. Always Remember!
If they are congruent, then set their measures equal to each other!

3. Goal 1: Bisecting a Segment
Midpoint: The point that bisects a segment.
Bisects?
splits into 2 equal pieces
A M B
12x x+5
12x+3=10x+5
2x=2
x=1

4. Segment Bisector
A segment, ray, line, or plane that intersects a segment at its midpoint. k A M B

5. Compass & Straightedge
Tools used for creating geometric constructions
We will do an activity with these later.

6. Midpoint Formula
Used for finding the coordinates of the midpoint of a segment in a coordinate plane.
If the endpoints are (x1,y1) & (x2,y2), then

7. Example: Find the midpoint of SP if S(-3,-5) & P(5,11).

8. Example: The midpoint of AB is M(2,4). One endpoint is A(-1,7)
Example: The midpoint of AB is M(2,4). One endpoint is A(-1,7). Find the coordinates of B.

9. Goal 2: Bisecting an Angle
Angle Bisector: A ray that divides an angle into 2 congruent adjacent angles.
BD is an angle bisector of <ABC. A D B C

10. Example: If FH bisects EFG & mEFG=120o, what is mEFH?

11. Last Example: Solve for x.
* If they are congruent, set them equal to each other, then solve!
x+40o
x+40 = 3x-20
40 = 2x-20
60 = 2x
30 = x
3x-20o

12. Activity Time
Use your compass, protractor and straightedge to work on the three activities in this section.
Pg 33, 34, 36