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