SECTION 1.5 SEGMENT AND ANGLE BISECTORS

AN ANGLE BISECTOR IS THE RAY THAT DIVIDES (OR BISECTS) AN ANGLE INTO CONGRUENT ADJACENT ANGLES.

O

M

G

N

HOW CAN WE USE THIS INFORMATION ABOUT ANGLE BISECTORS?

(x+40)°

(3x – 20)°

P

Q

R S

A MIDPOINT IS THE POINT THAT DIVIDES (OR BISECTS) THE LINE SEGMENT INTO EQUAL PARTS. THE EQUAL PARTS ARE ALSO CALLED CONGRUENT SEGMENTS.

D

E3 m

3 m

L

To Bisect means to divide in ½

DL = LE

To be congruent means to be equal

DON’T FORGET ABOUT ANGLE ADDITION AND SEGMENT ADDITION POSTULATES!

CAN WE BISECT A LINE? WHY OR WHY NOT?

Take a minute to write down your response.

BACK TO MIDPOINTS!

You will sometimes see midpoints on a coordinate plane.

The MIDPOINT FORMULA will allow you to find

the x and y coordinates for the midpoint.

P(1,2)

Q(3,-2)

How do we find that midpoint?

MIDPOINT FORMULA

The x for the midpoint =

The y for the midpoint =

Add the 2 and divide by 2 (sound familiar?)

LET’S PRACTICE THE MIDPOINT FORMULA

A (5, 4) and B(3, 2)

A(-1, -9) and B(11, -5)

A(6, -4) and B(1, 8)

C(3, 0) and M(3,4)

D(5,2) and M(7,6)

E(-4,2) and M(-3,-2)

FIND THE MIDPOINT (M)FIND THE ENPOINT