Transcript 1.5 Segment & Angle Bisectors

1.5 Segment &
Angle Bisectors
Always Remember!
• If they are congruent, then set
their measures equal to each
other!
Goal 1: Bisecting a Segment
• Midpoint: The point that bisects a
segment.
• Bisects?
splits into 2 equal pieces
A
12x+3
12x+3=10x+5
2x=2
x=1
M
10x+5
B
Segment Bisector
• A segment, ray, line, or plane that
intersects a segment at its midpoint.
k
A
M
B
Compass & Straightedge
• Tools used for creating geometric
constructions
• We will do an activity with these later.
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
Example: Find the midpoint of SP if
S(-3,-5) & P(5,11).
  3  5  5  11
,


2 
 2
2 6
 , 
 2 2
1,3
Example: 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
Goal 2: Bisecting an Angle
• Angle Bisector: A ray that divides an angle
into 2 congruent adjacent angles.
A
D
B
C
BD is an angle
bisector of <ABC.
Example: 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
Activity Time
• Use your compass, protractor and
straightedge to work on the three
activities in this section.
• Pg 33, 34, 36