1.2 Linear Measure and Precision
1.2 Linear Measure and Precision
Objectives:
 Measure segments and determine
accuracy of measurement
1.2 Linear Measure and Precision
Objectives:
 Measure segments and determine
accuracy of measurement
 Compute with measures
1.2 Linear Measure and Precision
A line segment CAN be measured (unlike
a line or ray) because it has 2 endpoints
1.2 Linear Measure and Precision
A line segment CAN be measured (unlike
a line or ray) because it has 2 endpoints
F
G
m
1.2 Linear Measure and Precision
Precision: Depends on the SMALLEST
unit available on the measuring tool.
Measurement should be precise to within 0.5
unit of measure
1.2 Linear Measure and Precision
Precision: Depends on the SMALLEST unit
available on the measuring tool.
Measurement should be precise to within 0.5
unit of measure
7 cm means that the ruler was divided into 1 cm –
it could be 6.5 cm to 7.5 cm in actual length
1.2 Linear Measure and Precision
Precision: Depends on the SMALLEST unit
available on the measuring tool.
Measurement should be precise to within 0.5
unit of measure
8.5 cm means that the ruler was divided into ½ cm
– it could be 8.25 cm to 8.75 cm in actual length
1.2 Linear Measure and Precision
Estimate the length of this rectangle.
about 4.5 cm
Smallest unit is 1mm
So precision is ± ½ mm
45 mm ± .5 mm  44.5 to 45.5 mm
1.2 Linear Measure and Precision
 What does the measurement “5 inches” mean?

1 inch increments

½ of 1 = ½

Range: 5 – ½ = 4.5 in.

5 + ½ = 5.5 in.
 8 ½ inches?
 ½ inch increments, therefore

(½ ) of (½ ) = ¼ in.
 Precise to ¼ inch  add ¼ and subtract ¼
 Between 8 ¼ to 8 ¾ inches
1.2 Linear Measure and Precision
Measures are real numbers so all
operations can be used on them.
Use 2 endpoint letters to show measure of
a segment.
AB is a measure – a length
A
B
C
AB = 5 in. DB = 34 in.
AB + DB = 5 + 34 = 39 in.
CD
Is not a measurement (note bar)
D
1.2 Linear Measure and Precision
We know that part + part = whole
 This is true for line segments in Geometry –
 Called “Segment Addition Postulate”
A
10 cm
part
B 4 cm
+ part
= the whole
14 cm
C
1.2 Linear Measure and Precision
Betweenness of points: for any two
real numbers a and b, there is a real
number n between a and b such that
a<n<b
A
a
n
B
b
C
AB + BC = AC
A, B, C must be collinear and B must
be between A and C
1.2 Linear Measure and Precision
Find y and PQ if P is between Q and R;
PQ = 2y, QR = 3y + 1, and PR = 21.
P, Q and R are collinear
Draw a figure to represent this information
and solve.
Q
2y
P
21
3y + 1
2y + 21 = 3y + 1
20 = y
PQ = 2●20 = 40
R
1.2 Linear Measure and Precision
Congruent segments: Two segments
having the same measure.
If AB = CD, then AB  CD
B
5 cm
D
5 cm
A
C
If AB  CD, then AB = CD
1.2 Linear Measure and Precision
Homework:
1.2 page 17 12 - 45 multiples of 3,

46-49, 56, 57