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