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