Lesson 1-2
Linear Measure and Precision
Lesson Outline

Five-Minute Check

Then & Now and Objectives

Vocabulary

Key Concept

Examples

Lesson Checkpoints

Summary and Homework
Then and Now
You identified and modeled points, lines, and
planes. (Lesson 1–1)
• Measure segments and determine
accuracy of measurement
• Compute with measures
• Sum of the parts equals the whole
Objectives
• Measure segments
• determine accuracy of measurement
• Compute with measures
• Sum of the parts equals the whole
Vocabulary
• Precision – is equal to one-half the smallest unit on the
measuring tool
• Line Segment – has two end points and can be measured
• Betweenness of points – when a point is between two other
collinear points
• Between – b is between a and c when a < b < c or a > b > c
• Congruent segments – when segments have the same measure,
they are congruent ()
• Construction – methods of creating figures without the benefit
of measuring tools
• Equal – numbers (variable and equations) and measurements of
things are equal if the have the same values
Example 1a
Find the length of
.
The long marks are centimeters, and the shorter marks are
millimeters. There are 10 millimeters for each centimeter.
Answer:
is about 42 millimeters long.
Example 1b
Find the length of
.
The ruler is marked in centimeters. Point R is closer to the
5-centimeter mark than to 4 centimeters.
Answer:
is about 5 centimeters long.
Example 1c
C. Find the length of segment DE.
Each inch is divided into sixteenths. Point E is
closer to the 3-inch mark.
Answer: Segment DE is about 3 inches long.
Example 1d
D. Find the length of segment FG.
Each inch is divided into fourths.
Point G is closer to the 2 ¾ inch mark.
Answer: Segment FG is about 2 ¾ inches long.
Key Concept
• The equation above is also known by “the sum of the
parts is equal to the whole”
• Example: Distance from Abingdon to Marion is
equal to distance from Abingdon to Chilhowie and
from Chilhowie to Marion
Whole = Sum of its Parts
Any distance can be broken into pieces and
the sum of those pieces is equal to the whole
distance
14
11
A
B
6
C
D
32
The whole length, AD, is equal to the sum of its
parts, AB + BC + CD
AD = AB + BC + CD
32 = 11 + 14 + 6
Example 2a
Find XZ. Assume that the figure is not drawn to
scale.
___
XZ is the measure of XZ. Point Y is between X and
Z. XZ can be found by adding XY and YZ.
Betweenness of points
Substitution
Add.
Example 2b
Find LM.
LM is the measure of
.
Point M is between L and N.
Sum of parts
whole
Substitution
Subtract 2.6 from each side.
Simplify.
Answer:
is 1.4 centimeters long.
Example 2c
Find x and ST if T is between S and U, ST = 7x, SU = 45,
and TU = 5x – 3.
5x – 3
U
7x
T
S
Substitute known values.
Add 3 to each side.
Simplify.
Divide each side by 12.
Simplify.
Key Concept
• Congruent is more than just equal
– similar sign  to the equal sign =
– equal measures in line segments
– same shape and size (measure) in other things
Example 3
FONTS The Arial font is often used because it is easy
to read. Study the word time shown in Arial type.
Each letter can be broken into individual segments.
The letter T has two segments, a short horizontal
segment, and a longer vertical segment. Assume that
all segments overlap where they meet. Which
segments are congruent?
TIME
Answer: The five vertical segments in the letters T, I, M,
and E are congruent. The four horizontal
segments in T and E are congruent. The two
diagonal segments in the letter M are
congruent.
2 ¼ ½ ¾
3 ¼ ½ ¾
4
Precision
Precision – ½ the smallest unit of
measure on the measuring device
70°F
Smallest Unit of Measure = 1/8 th inch
Precision = (1/8)/2 = 1/16 th inch
60°F
String Length is 2 ¼ ± 1/16 or
between 2 3/16 and 2 5/16 inches long
50°F
1 ¼ ½ ¾
40°F
Smallest Unit of Measure = 2°F
Precision = (2°F)/2 = 1°F
Temperature is 60°F ± 1°F or
between 59°F and 61°F
Example 4a
Find the precision for 32¾ inches. Explain its meaning.
The measuring tool is divided into
-inch increments. Thus,
the measurement is precise to within
Answer: The precision is
be
inches to
inch.
inch. The measurement could
inches.
Example 4b
PRECISION Find the precision for each measurement.
Explain its meaning.
a. 88 millimeters
Answer: The precision is 0.5 millimeter. The measurement
could be 87.5 millimeters to 88.5 millimeters.
b.
Answer: The precision is
could be
inch. The measurement
inches to
inches.
Lesson Checkpoints
Summary & Homework
• Summary:
– The measure of a line segment is the sum of the
measure of its parts
WHOLE = SUM OF PARTS
– The precision of any measurement depends on
the smallest unit available on the measuring
device
Precision = ½ (Smallest Unit)
• Homework:
– pg 18-21: 17-19, 21-23