1.3 Segments and
Their Measures
Learning Targets:
I can use segment postulates.
I can use the Distance Formula to
measure distances.
Postulates vs. Theorems
Postulates – rules accepted without proof
 Theorems – rules that are proven

Find the distance between two points.

How would you measure the length to the
nearest millimeter of the following segment:
G____________________________H
Postulate 1 : Ruler Postulate

The points on a line can be matched one-to-one
with the real numbers. The real number that
corresponds to a point is the coordinate of the
point.

The distance between points A and B, written as
AB, is the absolute value of the difference between
the coordinates of A and B.

AB is also called the length of segment AB.
Postulate 1 in simple terms…

Basically, you can find the length or distance of
a line segment by measuring it.
Postulate 2:
Segment Addition Postulate

Two friends leave their homes and walk in a
straight line toward the other’s home. When they
meet one has walked 425 yards and the other
has walked 267 yards. How far apart are their
homes?
Postulate 2:
Segment Addition Postulate

If B is between A and C, then AB + BC = AC

If AB + BC = AC, then B is between A and C
Postulate 2 in simple terms…

Basically, you can add the length of one
segment to the length of another segment,
to find the total length of the segments put
together.
Guided Practice

Two cars leave work and head towards
each other. When the two cars meet, the
first car has traveled 4.3 miles and the
second car has traveled 7.1 miles. How far
apart were the cars to begin with?
Using Postulate 2…

A, B, C, and D are collinear points. Find
BC if AC = 2x + 4, BC = x, BD = 3x + 1,
and AD = 17.
Guided Practice

W, X, Y, and Z are collinear points. Find
YZ if WX = 3x – 1, XY = 2x + 3, YZ = 5x,
and WZ = 42.
Sage and Scribe

Page. 21-22 #16 – 28 (Even Nos. Only)
#31-33 (ALL)
Answers to Sage and Scribe p 21-22
16. 2.7 cm
18. 3.4 cm
20. GH + HJ = GJ
22. QR + RS = QS
24. RS = 3
26. ST = 11
28. RT = 14
31. 4; 20, 3, 23
32. 13; 100, 43, 143
33. 1; 2.5, 4.5, 7
Objective:
• I can use the distance formula to find the
distance between two points.
The Distance Formula

The Distance Formula is a formula for
computing the distance between two
points in a coordinate plane.

The formula is:
d
=
Pythagorean Theorem Review

The sum of the squares of the two legs of
a triangle is equal to the square of the
hypotenuse (right triangles only)
c
a
b
a b  c
2
2
2
Practice

Find the length of the hypotenuse of a right
triangle with leg lengths of 9 ft and 12 ft.
c
9 ft
12 ft
y
 x1, y1 
x
 x2 , y2 
y
 x2 , y2 
d
 x1, y1 
x
y
 x2 , y2 
d
 x1, y1 
x2
x
y
 x2 , y2 
d
x1
 x1, y1 
x2
x
y
 x2 , y2 
d
x1
 x1, y1 
 x2  x1 
x2
x
y
 x2 , y2 
d
 x1, y1 
x
 x2  x1 
y
 x2 , y2 
d
 x1, y1 
x
 x2  x1 
y2
y
 x2 , y2 
d
 x1, y1 
x
 x2  x1 
y2
y1
y
 x2 , y2 
d
 x1, y1 
x
 y2  y1 
 x2  x1 
y2
y1
y
 x2 , y2 
d
 x1, y1 
x
 x2  x1 
 y2  y1 
y
 x2 , y2 
d
 x1, y1 
 y2  y1 
 x2  x1 
x
c  a b
2
2
2
d   x2  x1    y2  y1 
2
2
2
y
 x2 , y2 
d
 x1, y1 
 y2  y1 
 x2  x1 
x
c  a b
2
2
2
d   x2  x1    y2  y1 
2
2
2
y
 x2 , y2 
d
 y2  y1 
a
 x1, y1 
 x2  x1 
x
c  a b
2
2
2
d   x2  x1    y2  y1 
2
2
2
y
 x2 , y2 
d
 y2  y1 
a
 x1, y1 
 x2  x1 
x
c  a b
2
2
2
d   x2  x1    y2  y1 
2
2
2
y
 x2 , y2 
d
b y
2
 y1 
a
 x1, y1 
 x2  x1 
x
c  a b
2
2
2
d   x2  x1    y2  y1 
2
2
2
y
 x2 , y2 
d
b y
2
 y1 
a
 x1, y1 
 x2  x1 
x
c  a b
2
2
2
d   x2  x1    y2  y1 
2
2
2
d   x2  x1    y2  y1 
2
d
2
2
 x2  x1    y2  y1 
2
2
d   x2  x1    y2  y1 
2
d
2
2
 x2  x1    y2  y1 
2
2
 x1, y1   x2 , y2 
d
 x2  x1    y2  y1 
2
2
 x1, y1   x2 , y2 
d
 x2  x1    y2  y1 
2
2
x1 y1
x2 y2
 3, 1   2 , 4 
d
 x2  x1    y2  y1 
d
 2  3
2
2
  4  1
2
2
x1 y1
x2 y2
 3, 1   2 , 4 
d
 x2  x1    y2  y1 
d
 2  3
2
2
  4  1
2
2
x1 y1
x2 y2
 3, 1   2 , 4 
d
 x2  x1    y2  y1 
d
 2  3
2
2
  4  1
2
2
x1 y1
x2 y2
 3, 1   2 , 4 
d
 x2  x1    y2  y1 
d
 2  3
2
2
  4  1
2
2
x1 y1
x2 y2
 3, 1   2 , 4 
d
 x2  x1    y2  y1 
d
 2  3
2
2
  4  1
2
2
x1 y1
x2 y2
 3, 1   2 , 4 
d
 x2  x1    y2  y1 
d
 2  3
2
2
  4  1
2
2
x1 y1
x2 y2
 3, 1   2 , 4 
d
 x2  x1    y2  y1 
d
 2  3
2
2
  4  1
2
2
x1 y1
x2 y2
 3, 1   2 , 4 
d
 x2  x1    y2  y1 
d
 2  3
2
2
  4  1
2
2
x1 y1
x2 y2
 3, 1   2 , 4 
d
 x2  x1    y2  y1 
d
 2  3
2
2
  4  1
2
2
x1 y1
x2 y2
 3, 1   2 , 4 
d
 x2  x1    y2  y1 
d
 2  3
2
2
  4  1
2
2
x1 y1
x2 y2
 3, 1   2 , 4 
d
 x2  x1    y2  y1 
d
 2  3
2
2
  4  1
2
2
x1 y1
x2 y2
 3, 1   2 , 4 
d
 x2  x1    y2  y1 
d
 2  3
2
2
  4  1
2
2
x1 y1
x2 y2
 3, 1   2 , 4 
d
 x2  x1    y2  y1 
d
 2  3
d

2
1

2
  4  1
2
 3

2
2
2
x1 y1
x2 y2
 3, 1   2 , 4 
d
 x2  x1    y2  y1 
d
 2  3
d

2
1

2
  4  1
2
 3

2
2
2
x1 y1
x2 y2
 3, 1   2 , 4 
d
 x2  x1    y2  y1 
d
 2  3
d

2
1

2
  4  1
2
 3

2
2
2
d
d

1

2
 3
1  9

2
d
d

1

2
 3
1  9

2
d
d

1

2
 3
1  9

2
d
d

1

2
 3
1  9

2
d
d

1

2
 3
1  9
d  10

2
Using the Distance Formula

Find the lengths of the segments. Tell
whether any of the segments have the same
length.
Find distances on a city map


To walk from A to B you
can walk five blocks east
and three blocks north.
So…
What would the distance
be if a diagonal street
existed between the two
points?
Sage and Scribe
 Work
on page 22 :
#34 to 40 Even nos only
Homework

Work on #42 and #43 of page 22 of
Geometry book.