5'1 Perpendiculars and Bisectors

1
5.1 Perpendiculars and Bisectors

• Pg 264

2
? Bisector
l

• ? bisector a line, seg,ray or plane that is ? to
  a segment at its midpoint.
• A pt is equidistant from 2 pts if it is the same
  distance from each pt. (dont have to all be
  collinear)

__
A
_
B
M
3
Thm 5.1? bisector thm

• If a pt is on the ? bisector of a segment then it
  is equidistant from the endpts of the segment.

C
l
B
A
M
If l is the ? bisector of seg AB then CACB (and
DADB)
D
4
Thm 5.2Converse of the ? bisector thm

• If a pt is equidistant from the endpts of a
  segment then it is on the ? bisector

C
M
B
A

If CACB then C is on the ? bisector of AB
5
Given l is the ? bisectorProve ? ACM ? ? BCM
B
C
M
l
A
6
Proof

• Statements
• 1. l is the ? bisector
• 2. M is the midpt of seg AB
• 3. Seg AM _at_ seg BM
• 4. Seg AC _at_ seg BC
• 5. Seg CM _at_ seg CM
• 6. ? ACM _at_ ? BCM

• Reasons
• 1. given
• 2. Def of ? bisector
• 3. Def of a midpt
• 4. ? bisector thm
• 5. Reflex prop of seg _at_
• 6. SSS

7
Distance from a pt to a line

• Distance from a pt to a line- the length of the ?
  seg from the pt to the line.
• PDdistance from P to line l

P

l
D
8
Thm 5.3? bisector thm

• If a pt is on the bisector of an ? then it is
  equidistant from the sides of the ?.

D
A
)
O
)
G
9
Thm 5.4converse of the ? bisector

• If a pt is in the interior of an ? and is
  equidistant from the sides then it is on the ?
  bisector.

10
Assignment