Sec' 1 5 Measuring Segments

1
Sec. 1 5 Measuring Segments

• Objectives
• 1) Finding the lengths of segments.

2
Geometry vs Algebra

• Segments are Congruent
• Symbol ?
• AB ? CD
• ?1 ? ?2
• Lengths of segments are equal.
• Symbol
• AB CD
• m?1 m?2

?

3
Ruler Postulate

• P(1 5) The points of a line can be put into
  onetoone correspondence with the real numbers
  so that the distance between any two points is
  the absolute value of the difference of the
  corresponding numbers.
• AB

A
B
a
b
Coordinate of A
Coordinate of B
AB a b
The measure of the length of the segment AB
(Its a number)
4cm
1cm
4
Ex.1 Find AB, CE, AC
A
C
B
E
0
2
4
6
8
-2
-4
-6
-8
AC -8 -5 -8 5 -3
3
AB -8 5 -13 13
CE -5 6 -11 11
5
Segment Addition Postulate

• P (1 6) If 3 points A, B, C are collinear
  B is between A C, then
• AB BC AC

C
B
A
6
Ex.2 Find the length of the missing segment
L
M
N

• Find MN if
• LN 20
• LM 15
• Find DS if
• DT 60
• DS 2x 8
• ST 3x 12

15
LM MN LN 15 MN 20 MN 5
20
D
S
T
2x - 8
3x - 12
60
DS ST DT (2x - 8) (3x -12) 60 5x 20
60 x 16
DS 2x 8 DS 2(16) 8 DS 24
7

• Midpoint Is a point that divides a segment into
  two ? parts.
• RS ? ST
• RS ST
• Ex.3 Find AC CB if C is the Midpoint of AB.
• AC 2x 1
• CB 3x 4

R
S
T
A
C
B
AC CB 2x 1 3x 4 5 x
AC 2x 1 AC 2(5) 1 AC 11
CB
8
What have we learned??

• Finding the length of segments
• DE -5 3 8

E
D
-5
3
0
Segment Addition
M
N
MN NP MP (5x 4) (2x 14) 80 7x 10
80 x 10
P
2x 14
5x - 4
80