a.
Fold a 3-inch by 5-inch index card
on one of its diagonals.
3 in.
MAKING SENSE
OF PROBLEMS
To be proficient in math,
you need to explain to
yourself the meaning of
a problem and look for
entry points to its solution.
ps
1
2
3
4
5
6
7
8
9
1 0
1 1
1 2
1 3
1 4
1 5
1 6
1 7
1 8
1 9
2 0
2 0
2 1
2 2
2 3
2 4
2 5
2 6
2 7
2 8
2 9
INCH
fold
3 0
CM
1
2
3
4
5
6
7
8
9
10
11
12

b.
Use the Pythagorean Theorem
to algebraically determine the
length of the diagonal in inches.
Use a ruler to check your answer.
c.
Measure the length and width of the index card in paper clips.
d.
Use the Pythagorean Theorem to algebraically determine the length of the diagonal
in paper clips. Then check your answer by measuring the length of the diagonal in
paper clips. Does the Pythagorean Theorem work for any unit of measure? Justify
your answer.
Measuring Heights Using Nonstandard Units
Work with a partner.
Consider a unit of length that is equal to the length of the
diagonal you found in Exploration 2. Call this length “1 diag.” How tall are you in
diags? Explain how you obtained your answer.
Communicate Your Answer
Communicate Your Answer
4.
How can you measure and construct a line segment?
5 in.

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12
Chapter 1
Basics of Geometry
What You Will Learn
What You Will Learn
Use the Ruler Postulate.
Copy segments and compare segments for congruence.
Use the Segment Addition Postulate.
Using the Ruler Postulate
In geometry, a rule that is accepted without proof is called a
postulate
or an
axiom
.
A rule that can be proved is called a
theorem
, as you will see later. Postulate 1.1 shows
how to find the distance between two points on a line.
1.2
Lesson
Using the Ruler Postulate
Measure the length of
—
ST
to the nearest tenth of a centimeter.
S
T
SOLUTION
Align one mark of a metric ruler with
S
. Then estimate the coordinate of
T
. For
example, when you align
S
with 2,
T
appears to align with 5.4.
S
T
cm
1
2
3
4
5
6
ST
=
∣
5.4
−
2
∣
=
3.4
Ruler Postulate
So, the length of
—
ST
is about 3.4 centimeters.
Monitoring Progress
Monitoring Progress
Help in English and Spanish at
BigIdeasMath.com
Use a ruler to measure the length of the segment to the nearest
1
—
8
inch.
1.
M
N
2.
P
Q
3.
U
V
4.
W
X
postulate,
p. 12
axiom,
p. 12
coordinate,
p. 12
distance,
p. 12
construction,
p. 13
congruent segments,
p. 13
between,
p. 14
Core Vocabulary
Core Vocabu
l
a
ry
Postulate
Postulate
Postulate 1.1
Ruler Postulate
The points on a line can be matched one to
one with the real numbers. The real number
that corresponds to a point is the
coordinate
of the point.
The
distance
between points
A
and
B
, written
as
AB
, is the absolute value of the difference
of the coordinates of
A
and
B
.
A
AB
AB
=
x
2
−
x
1
B
x
1
x
2
A
B
x
1
x
2
names of points
coordinates of points

Section 1.2
Measuring and Constructing Segments
13
Constructing and Comparing Congruent Segments
A
construction
is a geometric drawing that uses a limited set of tools, usually a
compass
and
straightedge
.