1.5 Segment & Angle 1.5 Segment & Angle BisectorsBisectors

1.5 Segment & Angle 1.5 Segment & Angle BisectorsBisectors

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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,

22121

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 & m<EFG=120o, what is

m<EFH?

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