Download - Notes 1.2
Measuring and Constructing Segments
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
Congruent Segments are segments that have the same sizw and same shape. Tick Marks are used to show congruence.
If B is between A and C,
• • • A B C
then AB + BC = AC.
EXAMPLE # 1 Using the Segment Addition Postulate
M is between N and O. Find X.
10 = 2x
NM + MO = NO
17 + (3x – 5) = 5x + 2
– 3x – 3x
3x + 12 = 5x + 2
12 = 2x + 2
–2 –2
2 2
5 = x
E is between D and F. Find DF.
EXAMPLE # 2 Using the Segment Addition Postulate
DE + EF = DF
(3x – 1) + 13 = 6x
– 3x – 3x
3x + 12 = 6x
12 = 3x
4 = x
12 = 3x
3
3
E is between D and F. Find DF.
EXAMPLE # 2 ContinuedUsing the Segment Addition Postulate
DF = 6x
= 24
= 6(4)
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.
Example 3: Using Midpoints to Find Lengths
D FE 4x + 6 7x – 9
4x + 6 = 7x – 9
6 = 3x – 9
15 = 3x
Step 1 Solve for x.
ED = DF
–4x –4x
+9 + 9
D is the midpoint of EF, ED = 4x + 6, and DF = 7x – 9. Find ED, DF, and EF.
3 3
15 = 3x
x = 5
D FE 4x + 6 7x – 9
ED = 4x + 6
= 4(5) + 6
= 26
DF = 7x – 9
= 7(5) – 9
= 26
EF = ED + DF
= 26 + 26
= 52
Step 2 Find ED, DF, and EF.
D is the midpoint of EF, ED = 4x + 6, and DF = 7x – 9. Find ED, DF, and EF.
Example 3 Continued