1. Sec 1-2 Concept: Using Segments and Congruence
Obj: given the segment addition postulate, find the length of a segment as measured by a s.g.

2. Postulate 1: Ruler Postulate
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 AB AB A B X2 x1
AB = l x2-x1 l

3. Example 1: A B Find the length of AB AB = l 2-(-3) l = l 5 l = 5 1 2 31 2 3 -1 -2 -3
AB = l 2-(-3) l
= l 5 l
= 5

4. 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. A B C

5. Their houses are 692 yds apart
Example 2:
Two friends leave their homes and walk in a straight line towards the other’s home. When they meet one has walked 425 yds and the other has walked 267 yds. How far apart are their homes? A B C
267
425
AB + BC = AC
= AC
692 = AC
Their houses are 692 yds apart

6. Example 3: In the diagram of collinear points, GK=24, HJ = 10, and GH=HI=IJ. Find each length
JK =
IG =
IK = 5 5 5 9 10 14

7. Example 4: Suppose M is between L and N
Example 4: Suppose M is between L and N. Use the segment addition postulate to solve for the variable. Then find the lengths of LM, MN and LN
LM = 3x+8
MN = 2x-5
LN =23
LM = 7y +9
MN = 3y + 4
LN = 143
143 23 L M N L M N
7y+9
3y+4
3x+8
2x-5
(7y+9) + (3y+4) = 143
10y + 13 =143
10y = 130
y=13
(3x+8) + (2x-5) = 23
5x+3=23
5x=20
X=4
MN=3y+4
3(13)+4 43
LM = 3x+8
3(4)+8 20
MN = 2x-5
2(4)-5 3
LM=7y+9
7(13)+9
100

8. A(0,1), B(4,1), C(1,2), D(1,6); AB and CD?
Example 5: Plot the given points in a coordinate plane. Then determine whether the line segments named are congruent.
A(0,1), B(4,1), C(1,2), D(1,6); AB and CD? D
AB = 4
CD=4
Yes they are congruent C A B

9. Today’s Work
In Class:
Homework: