1. 1.5 Segment & Angle Bisectors
Geometry

2. Standard/Objective
Standard 3: Students will understand geometric concepts and applications.
Objectives:
Bisect a segment.
Bisect an angle.

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

4. 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

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

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

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

9. 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. Ex: 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