Midpoints and BisectorsVocabulary found in Chapter 1 Section 5

Midpoint, Perpendicular lines, Segment Bisector, Perpendicular Bisector, Angle Bisector.

A M B

- If AM = MB, then M is the midpoint of AB.

- If M is the midpoint of AB, then AM = MB. ~~

~

C

1. If M is the midpoint of AB and B is the midpoint of MC, write an argument of why AM = BC. Include your reasoning.

C B

DAAB CD

(read: AB is perpendicular to CD)

If , then all of the angles formed at the point of intersection are right angles.

2. What could you conclude if you were told that two lines intersected to form 90° angles? 60° and 120° angles?

- It does not mean that JZ = ZK~

An angle bisector is a line, segment or ray that divides an angle into two congruent angles.

M

H

TA

1

2

YX

K

J

Z- If JK is a perpendicular bisector of XY, then the angles all measure 90 , and Z is the Mid. Pt. of XY. Furthermore XZ = ZY.

o

~

A segment bisector is a line, segment or ray that intersects a segment at its midpoint.

VS E

T

OFinish these Statements:

E is the Mid. Pt. of SO.

SE = EO~If E is the Mid. Pt. of SO, then ____________

If TV bisects SO, then ___________________

- If AT is an angle bisector of MAH, then 1 = 2.~

1. If M is the midpoint of AB, then AM = MB. (By Def. of a Midpoint) If B is the midpoint of MC, then MB = BC. (By Def. of a Midpoint) If AM = MB and MB = BC, then AM = BC by the Transitive Property

~~

~~ ~

2. If two lines intersected to form 90° angles, then they are Perpendicular. If two lines intersected to form 60° or 120° angles, then they are not Perpendicular