Download 1.4 Measuring Segments and Angles

1.3 Measuring Segments and
Angles
Postulate 1-5
Ruler Postulate
The distance between any two points is the absolute
value of the difference of the corresponding
numbers (on a number line or ruler)
Congruent Segments: two segments with the same
length
Congruent Symbol:

Postulate 1-6
Segment Addition Postulate
If three points A, B, and C are collinear and B is
between A and C, then AB + BC = AC
C
B
A
Using the Segment Addition Postulate
If DT = 60, find the value of x. Then find DS and ST.
2x - 8
D
3x - 12
S
T
So if…
DT  60
Then…
60  (2 x  8)  (3x  12)
and
60  5x  20
80  5x
16  x
DT  DS  ST
DS  2x  8
DS  2(16)  8
DS  24
ST  3x 12
ST  3(16)  12
ST  36
Using the Segment Addition Postulate
If EG = 100, find the value of x. Then find EF and FG.
4x - 20
E
EG  EF  FG
100  (4 x  20)  (2 x  30)
100  6x  10
90  6x
15  x
2x + 30
F
G
EF  4x  20
EF  4(15)  20
EF  40
FG  2x  30
FG  2(15)  30
FG  60
Midpoint: a point that divides the segment into
two equal parts
A
B
C
B is the midpoint, so AB = BC
Note: any point line or ray that goes through
the midpoint of a segment is called a segment bisector
Finding Lengths
C is the midpoint of AB. Find AC, CB, and AB.
3x – 4
2x + 1
A
AC  CB
2x 1  3x  4
1 x 4
x 5
C
CB  AC  2x  1
CB  AC  2(5)  1
CB  AC  11
B
AB  AC  CB
AB  11 11
AB  22
Z is the midpoint of XY, and XY = 27. Find XZ.
27
X
Z
XZ  ZY
Meaning Z is HALF the distance of XY so…
XY
XZ 
2
27

2
 13.5
Y