Transcript 1.5 Segment & Angle Bisectors

1.5
Segment &
Angle Bisectors
Goals:
Students will understand geometric concepts
and applications.
 Bisect a segment.
 Bisect an angle.
Remember!
 Congruent means,…
 equal to each other!
Midpoint
 The point that bisects a segment.
 Bisects?
splits into 2 equal pieces
12x+3=10x+5
2x=2
x=1
A
12x+3
M
10x+5
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
H
F
120
 60 o
2
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