1. 1.5 Segment & Angle
Bisectors
p.34

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

3. Midpoint
• The point that bisects a segment.
• Bisects?
splits into 2 equal pieces
12x+3 10x+5
A M B
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 a project 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
 x1 + x2 y1 + y2 
 , 
 2 2 

7. Ex: Find the midpoint of SP if S(-3,-5) &
P(5,11).
 − 3 + 5 − 5 +11 
 , 
 2 2 
2 6 
 , 
2 2 
(1,3)

8. Ex: The midpoint of AB is M(2,4). One endpoint
is A(-1,7). Find the coordinates of B.
 x1 + x2 y1 + y2 
 ,  = (midpoint )
 2 2 
x1 + x2 y1 + y2
=2 =4
2 2
− 1 + x2 7 + y2
=2 =4
2 2
− 1 + x2 = 4 7 + y2 = 8
x2 = 5 y2 = 1
( 5,1)

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

10. Ex: If FH bisects <EFG &
m<EFG=120o, what is m<EFH?
E
120
H = 60 o
2
F
G
m < EFH = 60 o

11. Last example: Solve for x.
* If they are
congruent, set them
equal to each other,
then solve!
o
0
x +4 x+40=3x-20
o
3x-20 40=2x-20
60=2x
30=x

12. Assignment