1. Measuring and Constructing Segments
Notes 1.2
Measuring and Constructing
Segments

2. Distance
The Distance between any 2 points is the absolute value of the difference of the coordinates.
BC = |C – B| = |3 – 1| = 2
AC = |C – A| = |3 - -2| = |3 + 2| = 5

3. Congruent Segments
Congruent Segments are segments that have the same sizw and same shape.
Tick Marks are used to show congruence.

4. SEGMENT ADDITION POSTULATE
If B is between A and C,
• • •
A B C
then AB + BC = AC.

5. Using the Segment Addition Postulate
EXAMPLE # 1
Using the Segment Addition Postulate
M is between N and O. Find X.
NM + MO = NO
17 + (3x – 5) = 5x + 2
3x + 12 = 5x + 2
– 3x – 3x
12 = 2x + 2
– –2
10 = 2x 2
5 = x

6. 4 = x EXAMPLE # 2 Using the Segment Addition Postulate
E is between D and F. Find DF.
DE + EF = DF
(3x – 1) + 13 = 6x
3x + 12 = 6x
– 3x – 3x
12 = 3x
12 = 3x 3
4 = x

7. Using the Segment Addition Postulate
EXAMPLE # 2 Continued
Using the Segment Addition Postulate
E is between D and F. Find DF.
DF = 6x
= 6(4)
= 24

8. Midpoints
The midpoint M of AB is the point that bisects, or divides, the segment into two congruent segments.
Example:
If M is the midpoint of AB, then AM = MB.
So if AB = 6, then AM = 3 and MB = 3.

9. Example 3: Using Midpoints to Find Lengths
D is the midpoint of EF, ED = 4x + 6, and DF = 7x – 9. Find ED, DF, and EF. E D
4x + 6
7x – 9 F
Step 1 Solve for x.
ED = DF
15 = 3x
4x + 6 = 7x – 9
–4x –4x
6 = 3x – 9
x = 5
15 = 3x

10. Example 3 Continued
D is the midpoint of EF, ED = 4x + 6, and DF = 7x – 9. Find ED, DF, and EF. E D
4x + 6
7x – 9 F
Step 2 Find ED, DF, and EF.
ED = 4x + 6
DF = 7x – 9
EF = ED + DF
= 4(5) + 6
= 7(5) – 9 =
= 26
= 26
= 52