Transcript 1.5 Segment & Angle Bisectors - Belle Vernon Area School

1.5 Segment & Angle Bisectors
Always Remember!
• If they are congruent, then set their
measures equal to each other!
Midpoint
• The point that bisects a segment.
• Bisects?
splits into 2 equal pieces
12x+3
A
12x+3=10x+5
2x=2
x=1
10x+5
M
B
Segment Bisector
• A segment, ray, line, or plane that
intersects a segment at its midpoint.
k
A
M
B
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
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
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
2
2
7  y2
4
2
1  x2  4
7  y2  8
x2  5
y2  1
5,1
Angle Bisector
• A ray that divides an angle into 2 congruent
adjacent angles.
A
D
B
C
BD is an angle
bisector of <ABC.
Ex: If FH bisects <EFG & m<EFG=120o,
what is m<EFH?
E
120
 60 o
2
H
F
m  EFH  60
o
G
Last example: Solve for x.
* If they are
congruent, set them
equal to each other,
then solve!
x+40=3x-20
40=2x-20
60=2x
30=x