1. Section 1 - 3
Measuring Segments

2. Things You Might Already Know
Coordinate
A numerical location
Can be given in one of three ways
A single relative marker (for linear use)
An ordered pair (x ,y) (for planar use)
An ordered triple (x, y, z) (for spatial use)
Distance
The linear difference between two coordinates
You have to subtract

3. Your First Formula To determine a segment length
Where AB is the segment in question
a and b are the numerical coordinates A B b a

4. Your First Formula Example Determine the length of segment ST
Find the length of segments UV and SV S -2 -4 12 14 2 4 10 U 8 6 T V

5. A Sprinkle of Algebra The Segment Addition Postulate AB + BC = AC
Find AC if AB = 4 and BC = 7
AC = 11
Find AB if AC = 14 and BC = 6
AB = 8
BIG TIP  When given a drawing, do not base assumptions on the drawing itself. Instead use what is on the drawing. A B C

6. Example 1 If EG = 59, find EF and FG
Use the Segment Addition Postulate
EF + FG = EG
8x – x + 1 = 59
12x – 13 = 59
12x = 72
x = 6

7. But Wait, There’s More Now we must find what we were asked for
EF = 8x – 14
EF = 8(6) – 14
EF = 48 – 14
EF = 34
FG = 59 – 34
FG = 25

8. Example 2 If EG = 120, find EF and FG
Use the Segment Addition Postulate
EF + FG = EG
4x x + 15 = 120
11x + 21 = 120
11x = 99
x = 9

9. Example 2 cont. EF = 4x + 6 EF = 4(9) + 6 EF = 36 + 6 EF = 42
FG = 120 – 42
FG = 78

10. A Potential Shortcut Congruence On a Number Line
Congruent is the adjective
Two or more associated figures are identical
The symbol for congruent is
On a Number Line
Are TU and UV congruent? S -2 -4 12 14 2 4 10 U 8 6 T V

11. A Potential Shortcut Use Distance to check for congruence
Since both distances are the same, the segments are congruent

12. The Use Bisect To cut in half To cut into two congruent parts
If the bisecting is done by a point, it is referred to as a midpoint
Mathematically, the two segments are equal to each other

13. Example 3 Find PR if Q is the midpoint
Set the segments equal to each other
PQ = QR
6x – 7 = 5x + 1
6x = 5x + 8
-5x -5x
x = 8
PQ = 6x – 7
PQ = 6(8) – 7
PQ = 48 – 7
PQ = 41
PR = 2PQ
PR = 82
6x – 7
5x + 1 P Q R

14. Assignment
Pg 24
8 - 28