1. 1.3 Segments and Their Measures
Objectives:
Use the Segment Addition Postulate.
Use the Distance Formula to find the distance between two points.

2. Basic Vocabulary Postulate Theorem
a rule that is accepted as true without proof
Theorem
a rule that must be proven true.

3. Postulates Ruler Postulate AB = | x2 – x1 | names of the points A B x1
coordinates of the points
AB = | x2 – x1 |
The distance between points A and B or the length of AB

4. This indicates that the points are collinear.
Postulates
Segment Addition Postulate
If B is between A and C
then AB + BC = AC A B C
This indicates that the points are collinear.

5. add up to the whole segment.
Postulates
Segment Addition Postulate
If B is between A and C
then AB + BC = AC A B C AB BC AC
The pieces of a segment
add up to the whole segment.

6. The postulate also works in reverse
Postulates
Segment Addition Postulate
If A, B , and C are collinear and AB + BC = AC
then B is between A and C A B C AB BC AC
The postulate also works in reverse

7. Example 1: E D F

8. Example 2: x E x 9 D 35 C B A

9. Practice 1: x 2x D 2 C 20 B A

10. Example 3: Find the distance between Sue’s house and Jane’s house.
425 yds
267 yds
692 yds

11. Example 4: 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?
12 feet
15 feet
27 – 15
27 feet

12. Theorem The Distance Formula If A(x1, y1) and B(x2, y2) are points on
a coordinate plane
then the distance between
A and B is x y A B C

13. Definition Congruent Segments segments that have the same length B Y AX
the symbol for congruent
this represents a number equal to a number
this represents a figure the same size and shape as another figure

14. Example 5: Find the lengths of the segments.
Are any of the segments congruent? x y

15. Example 5: Find the lengths of the segments.
Are any of the segments congruent? x y

16. none of the segments are congruent
Example 5:
none of the segments are congruent
Find the lengths of the segments.
Are any of the segments congruent? x y

17. Practice 3:
Find the distance between the points. A (3, 1) B (0, 4)

18. Summary What is a postulate? Describe how to use the Distance Formula
Describe how to use the Segment Addition Postulate.
Describe how to use the Distance Formula