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1.3 Segments and Their Measures
Objectives:1.Use the Segment Addition Postulate.
2.Use the Distance Formula to find the distance between two points.
Basic Vocabulary
Postulate a rule that is accepted as true without proof
Theorem a rule that must be proven true.
x2
Postulates
1. Ruler Postulate
A Bx1
names of the points
coordinates of the points
AB = | x2 – x1 |
The distance between points A and B or the length of AB
This indicates that the points are collinear.
2. Segment Addition PostulateIf B is between A and C
then AB + BC = AC
Postulates
A B C
2. Segment Addition PostulateIf B is between A and C
then AB + BC = AC
Postulates
A B C
AB BC
ACThe pieces of a segment
add up to the whole segment.
2. Segment Addition Postulate
Postulates
A B C
AB BC
AC
then B is between A and C If A, B , and C are collinear and AB + BC = AC
The postulate also works in reverse
Draw a sketch of the three collinear points, , , and where is between and .
Write the Segment Addition Postulate for the three points.
D E F D E F
Example 1:
E FD
ED DF EF
Example 2:
AB
CD
E
CD DE
35AE
Find DE
9AC 9 35x x
AC CD CE AC
x
9
35
x
13x 2 9 35x
Practice 1:
AB
CD
20AD
Find BC
2AB 2 2 20x x
AB BC CD AD
x
2
20
2x
6x 3 2 20x
2BC xCD x
12BC
Example 3:
Find the distance between Sue’s house and Jane’s
house.
425 yds267 yds
425 + 267
692 yds
A truck with a trailer has a total length of 27 feet. If the trailer has a length of 15 feet,how long is the truck?
27 – 1512 feet
Example 4:
27 feet15 feet
The Distance FormulaIf A(x1, y1) and B(x2, y2) are points on a coordinate plane
then the distance between A and B is
Theorem
x
y
A
BC
2 2
2 1 2 1AB x x y y
AB XYAB XY
Definition
Congruent Segments segments that have the same length
A B X Y
this represents a number equal to a number
this represents a figure the same size and
shape as another figure
the symbol for congruent
2 21 3 2 3
2 2
2 1 2 1x x y y
1,2F
=EF
Find the lengths of the segments.Are any of the segments congruent?
Example 5:
x
y
2 24 1
16 117
3,3E
0, 1H 3,0G
1,2F
2 5
2 2
2 1 2 1x x y y
2 23 1 0 2
2 24 2
16 4 20
Find the lengths of the segments.Are any of the segments congruent?
Example 5:
x
y =FG 3,3E
0, 1H 3,0G
1,2F
2 2
2 1 2 1x x y y
2 20 3 1 0
2 23 1
9 1 10
=GH
Find the lengths of the segments.Are any of the segments congruent?
Example 5:
x
y
none of the segments are congruent
3,3E
0, 1H 3,0G
Practice 3:
Find the distance between the points. A (3, 1) B (0, 4)
2 2
2 1 2 1x x y y
2 20 3 4 1 2 2
3 3
9 9
=AB
18 9 2 3 2
Summary
What is a postulate?
Describe how to use the Segment Addition Postulate.
Describe how to use the Distance Formula