1.5 Segment & Angle Bisectors
GeometryFall 2005Mrs. Spitz
Standard/Objective
Standard 3: Students will understand geometric concepts and applications.
Objectives:
• Bisect a segment.
• Bisect an angle.
Assignment:
• pp. 38-40 #2-48 Even and
• Practice Quiz – pg. 42 #1-6 all
Always Remember!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
A M B 12x+3 10x+5
12x+3=10x+5
2x=2
x=1
Segment Bisector
• A segment, ray, line, or plane that intersects a segment at its midpoint.
A
BM
k
Compass & Straightedge
• Tools used for creating geometric constructions
• We will do a project 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
2,
22121 yyxx
Ex: Find the midpoint of SP if S(-3,-5) & P(5,11).
2
115,
2
53
2
6,
2
2
3,1
Ex: The midpoint of AB is M(2,4). One endpoint is A(-1,7). Find the coordinates of B.
)midpoint(2
,2
2121
yyxx
22
21 xx
42
21 yy
22
1 2 x
42
7 2 y
41 2 x 87 2 y
52 x 12 y
1,5
Angle BisectorAngle Bisector
• A ray that divides an angle into 2 congruent adjacent angles.
BD is an angle bisector of <ABC.
B
A
C
D
Ex: If FH bisects EFG & mEFG=120o, what is mEFH?
G
H
E
F
o602
120
oEFHm 60
Last example: Solve for x.
x+40o
3x-20o
* If they are congruent, set them equal to each other,
then solve!
x+40 = 3x-20
40 = 2x-20
60 = 2x
30 = x