1. Measure Line Segments
Unlike a line, a line segment, or segment, can be measured because it has
two endpoints. A segment with endpoints A and B can be named AB or
BA. The length or measure of AB is written as AB A B mm 1 2 3 4
AB is about 28 millimeters long.

2. Calculate Measures
Measures are real numbers, so all arithmetic operations can be used with them. We know that the whole usually equals the sum of its parts. This is also true of line segments in geometry.
Betweenness of Points
Point M is between points P and Q if and only if P, Q, and M are collinear and PM + MQ = PQ Q M P

3. Example 1 - Find Measurements
1. Find AC
AC is the measure of AC A
3.3 cm B
3.4 cm C
AC can be found by adding AB and BC
AB + BC = AC Sum of the parts = whole
= AC Substitution
6.7 = AC Add

4. Example 2 - Find Measurements
2. Find DE
DE is the measure of DE F 3 E D 12
AC can be found by adding AB and BC
DE + EF = DF Sum of the parts = whole
DE = Substitution
DE = Subtract 3 from each side
DE = Simplify

5. Example 3 - Find Measurements
3. Find y and PQ if P is between Q and R, PQ = 2y, QR = 3y + 1, and PR = 21
3y + 1 2y 21 Q P R
QR = QP + PR
3y + 1 = 2y + 21 Substitute known values
3y = 2y + 21 – 1 Subtract one from each side
3y = 2y + 20 Simplify
3y – 2y = 2y + 20 – 2y Subtract 2y from each side
y = 20 Simplify
PQ = 2y Given
PQ = 2(20) y = 20
PQ = 40 multiply

6. Key Concept Congruent Segments Words
Two segments having the same measure are congruent
Model XY = PQ
Symbol
= is read is congruent to
Red slashes on the figure also indicate that the segments are congruent Y X P Q

7. Example 4 - Find Measurements
Find RS and ST
6x - 5
2x + 3 R S T 30

8. Example 5 - Find Measurements
Find a, RT 7a
12a R S T 28

9. Example 6 - Find Measurements
Find x, RS and ST 2x 3x R S T 25

10. Example 7 - Find Measurements
Find x, RS and ST
3y + 1 2y R S T 21

11. Example 8 - Find Measurements
Find x, RT and ST 12 2x R S T
5x + 10

12. Example 9 - Find Measurements
Find y, RS and ST
4y - 1
2y - 1 R S T 5y