1. No category

Donovan Reese/Getty Images
Contents
SCAS
5-6.3; 5-6.4
Lesson 7-1
5-6.5, 5-6.6
Lesson 15-2 Probability as a Fraction
Mean, Median, Mode
5-5.1
Reading a Ruler to _ Inch (Use after Lesson 12-1)
5-4.3
Classify Congruent Shapes (Use after Lesson 13-4)
5-4.2; 5-4.3
Congruent Shapes (Use after Lesson 13-3)
1
8
Donovan Reese/Getty Images
1
Reading a Ruler to _ Inch
8
MAIN IDEA
I will measure length
to the nearest eighth
inch.
SC Academic Standards
5-5.1 Use
appropriate tools and
units to measure
objects to the
precision of
one-eighth inch.
Sometimes it is necessary to
measure objects to a small
unit, such as an eighth of an
inch. A smaller unit of measure
will give a more precise
measurement. Some projects,
such as building a birdhouse,
will require precise
measurements.
Length is the measurement of distance between two points.
You can use a ruler like the one below to measure the length
of objects to the nearest quarter inch or eighth inch. Each of the
smallest marks on the ruler represents an eighth of an inch.
SC Math Online
macmillanmh.com
• Extra Examples
• Personal Tutor
• Self-Check Quiz
JODIFT
EXAMPLE
Measure to the Nearest Eighth Inch
1 Find the length of a nickel
to the nearest eighth inch.
Place the ruler against one
edge of the object. Line up
the zero on the ruler with
the end of the object.
JODIFT
7
8
Find the eighth-inch mark
that is closest to the other end.
7
To the nearest eighth inch, the nickel is _ inch long.
8
692
Real-World EXAMPLE
Measure Length
2 ELECTRONICS Measure the MP3 player’s length to the
nearest eighth inch.
3
The MP3 player is between 1_ inches
4
3
7
and 1_ inches. It is closer to 1_ inches.
4
MENU
8
3
The length of the MP3 player is about 1_ inches.
4
You can also use an inch ruler to draw a line segment to a
given length.
EXAMPLE
Draw a Line Segment
3 Draw a line segment measuring 2
Draw a line
segment
7
from 0 to 2_.
8
0
in.
_7 inches.
8
3
2
1
Measure the length of each of the following to the nearest eighth of an inch.
(See Examples 1-2, pp. 692-693)
1.
2.
3.
Draw a line segment of each length. (See Example 3, p. 693)
7
4. _ inch
8
5. 2_ in.
5
8
6. Use a ruler to measure the width of your thumb to the nearest eighth inch.
1
Reading a Ruler to _ Inch
8
693
Measure the length of each of the following to the nearest eighth of an inch.
(See Examples 1-2, pp. 692-693)
7.
8.
9.
10.
11.
12.
13.
14.
15.
Draw a line segment of each length. (See Example 3, p. 693)
5
16 _ in.
8
3
17 1 _ in.
8
Measure the length of each line segment to the nearest eighth inch.
18.
19.
20. Draw a line that is between 5 and 6 inches long. Measure the
length to the nearest eighth inch.
21. Measure the length of the crayon to the nearest eighth inch. Then
measure the length of the pencil to the nearest eighth inch. Which
measure is closer to the actual length? Explain your reasoning.
694
HATS The table below shows the measurements that a hat
maker uses to determine hat size.
Hat Size
Head
Circumference (in.)
6_
6_
7_
7_
7_
7_
8
20_ 20_ 21_ 21_ 21_ 22_ 22_
23
23_ 23_ 24_ 24_
25
5
8
1
2
6_
3
4
1
4
3
4
1
8
6_
7
8
1
2
7_
1
8
7
7
8
1
4
1
4
5
8
3
8
1
2
1
2
7_
7_
5
8
3
4
7
8
1
4
7
8
5
8
22. Josie used a tape measure and measured her head to have a
1
circumference of 21_ inches. What size hat should she buy?
8
1
23. Pablo’s hat size is 7_. What is his head circumference?
4
1
24. Mr. Benkey measured his head to be 23_ inches. What size
8
hat will fit him best?
25. OPEN ENDED Draw a segment that is between 3_ inches
2
1
and 4_ inches. What is the measure of the segment to the
2
nearest fourth inch? What is the measure to the nearest
eighth inch?
1
26. CHALLENGE Suppose you know that a line is 4_ inches long
4
when measured to the nearest quarter inch. What do you
know about the actual length of the line?
3
27. REASONING Measure the length of the pansy at the right to
the nearest inch, nearest half inch, nearest fourth inch, and
nearest eighth inch. Which measure is the most precise?
What would be an even more precise measure?
28. WHICH ONE DOESN’T BELONG?
Which of the following measurements does not describe the
length of the line segment? Explain your reasoning.
3_41 inches
3 inches
3_81 inches
3_8 inches
5
Which is a more precise measurement:
29.
3
1
7_ inches or 7_ inches? Explain.
2
8
1
Reading a Ruler to _ Inch
8
695
Classify Congruent Shapes
HONEYCOMBS A honeycomb
is built by honey bees as a
nest to store their honey and
pollen. Each hexagon, or
6-sided figure, of the
honeycomb is the same shape
and size.
MAIN IDEA
I will determine
whether shapes are
congruent or
not congruent.
SC Academic Standards
5-4.3 Classify shapes
as congruent.
New Vocabulary
congruent shapes
In Lesson 13-1, you learned that line segments are congruent if
they have the same length. Two- and three-dimensional shapes
can also be congruent. Congruent shapes have the same size
and shape. The hexagon shapes in the honeycomb above are
congruent shapes.
SC Math Online
Congruent
Not Congruent
macmillanmh.com
• Extra Examples
• Personal Tutor
• Self-Check Quiz
EXAMPLES
Classify Two-Dimensional Shapes
Tell whether each pair of shapes is congruent or not
congruent.
1
2
The shapes have the
same size and shape.
They are congruent.
696
The shapes have the same
shape but not the same
size. They are not congruent.
In Lesson 14-4, you studied three-dimensional shapes.
Three-dimensional shapes can also be classified as
congruent or not congruent.
EXAMPLES
Classify Three-Dimensional Shapes
Tell whether each pair of shapes is congruent or not
congruent.
3
4
The rectangular prisms do
not have the same shape.
They do not have the same
size. They are not congruent.
The rectangular prisms
have the same size and
shape. They are congruent.
Tell whether each pair of shapes is congruent or not congruent.
(See Examples 1-4, pp. 696-697)
1.
2.
3.
4.
5. Briana created the two stars out of fabric for a
quilt she is making. She wants the two stars to
be the same shape and size. Tell whether the
shapes are congruent or not congruent. Explain
your reasoning.
Classify Congruent Shapes
697
Tell whether each pair of figures is congruent or not congruent. (See Examples 1-4, pp. 696-697)
6.
7.
8.
9.
10.
11.
12.
13.
14. Derek designed the two logos at the right. He
wants them to be the same size and shape. Tell
whether the shapes are congruent or not
congruent. Explain your reasoning.
15. A cereal company wants their cereal boxes to be the
same size and shape. Refer to the cereal boxes at the
right. Tell whether the shapes are congruent or not
congruent. Explain your reasoning.
16. CHALLENGE Which transformations studied in Chapter 13 result in
congruent shapes? Explain your reasoning.
17.
698
Write about a real-world situation in which
congruent shapes are used and necessary.
Congruent Shapes
Hands-On Mini Lab
MAIN IDEA
Step 1
Draw a triangle on a piece of
paper.
A
Step 2
Trace the triangle, so that it is
the same size and shape as
the first triangle. Cut out both
triangles. Label the angles as
shown.
C
I will identify congruent
angles, sides, and
perimeters of congruent
shapes.
SC Academic Standards
5-4.3 Classify shapes
as congruent.
5-4.2 Compare the
angles, side lengths,
and perimeters of
congruent shapes.
Step 3
B
X
Z
Y
Place one triangle over the other so that the
congruent angles match up.
1. Which angle matches up with angle A? angle B? angle C?
2. What conclusion can you make about the angles of
congruent triangles?
SC Math Online
macmillanmh.com
• Extra Examples
• Personal Tutor
• Self-Check Quiz
Key Concept
Congruent Shapes
Words
If two shapes are congruent,
they have the same angle
measures and side lengths.
Model
B
E
C
A
F
D
Symbols The symbol means congruent. ABC DEF
Congruent sides: AB DE; AC DF; BC EF
Congruent angles: ∠ A ∠D; ∠B ∠E; ∠C ∠ F
EXAMPLE
Congruent Parts of Congruent Shapes
1 IF Δ JKM ΔSTU, name the congruent sides and angles.
congruent sides:
JM SU; KM TU; JK ST
congruent angles:
∠ J ∠S; ∠K ∠T; ∠M ∠U
M
K
J
U
T
S
Congruent Shapes
699
If two shapes are congruent and you know the measurements
of one shape, you can determine the measurements of the
other shape. This can help you to find the perimeter of a
given shape.
EXAMPLE
Perimeter of Congruent Shapes
2 DOORS The doors shown
below are congruent. What is
the perimeter of the first door?
Since the doors are congruent,
their perimeters are the same.
Find the perimeter of the second
door.
P = 2l + 2w
Perimeter of a rectangle
P = 2(7) + 2(3)
l = 7 and w = 3
P = 14 + 6
Multiply.
P = 20
Add.
So, the perimeter of the first door is 20 feet.
Triangle ABC is congruent to ΔLMN.
Identify the part congruent to each
angle or line segment.
N
C
A
(See Examples 1-2, pp. 699-700)
1. ∠A
2. BC
3. ∠M
4. LM
M
B
5. Rectangle PQRS is congruent to rectangle ABCD. The
perimeter of rectangle PQRS is 16 meters. What is the
perimeter of rectangle ABCD?
6. For a winter-time decoration, the Darnell family strings lights
around the perimeter of their family room windows. The
windows are the same size and shape. If 17 feet of lights are
needed for one window, how many feet of lights are needed
for the other window?
700
L
Rectangle ABCD is congruent to rectangle
MNPQ. Identify the angle congruent to
each angle. (See Example 1, p. 699)
A
B
M
N
D
C
Q
P
7. ∠A
8. ∠P
9. ∠D
10. ∠B
Triangle GHI is congruent to ΔLKJ. Identify
the line segment congruent to each line
segment. (See Example 1, p. 699)
G
H
I
J
L
K
11. GH
12. IH
13. LJ
14. KL
Triangle XYZ is congruent to ΔDEF.
D
(See Example 2, p. 700)
X
15. What is the measure of side XY?
16. What is the measure of side YZ?
17. What is the perimeter of ΔXYZ?
Y
Z
F
E
18. The two rectangular windows in Danielle’s family room are
congruent. The dimensions of one of the windows is 40 inches
by 65 inches. What is the perimeter of each window?
19. Two rectangular gardens have the same shape and size.
Twenty-two feet of fence are needed to completely go
around one garden. How much fencing is needed for the
second garden?
20. Measurement Measure the side lengths of the
1
rectangle shown to the nearest _ inch. If you were
4
to draw a rectangle that is congruent to the one
shown, what will be the perimeter of the rectangle
you draw?
21. Two squares have the same perimeter, 32 feet. Find
the length of the sides of each square. Determine
whether the figures are congruent. Explain.
Congruent Shapes
701
Real-World PROBLEM SOLVING
QUILTS
When making a quilt, congruent
pieces of fabric are sewn and quilted together
to make a design.
E
B
A
21. What congruent shapes do you notice in
the quilt shown?
D
C
22. What side of 6ABC is congruent to EF ?
F
23. What angle of 6DEF is congruent to ∠A?
24. If the perimeter of 6DEF is 14.5 inches,
what is the perimeter of 6ABC ?
25. OPEN ENDED Draw a pair of congruent triangles. Label the
vertices of the triangles. Using these labels, write three
congruent statements about the triangles.
26. CHALLENGE Triangle ABC has side lengths of 6 centimeters,
11 centimeters, and x centimeters. Triangle ABC is congruent
to ΔXYZ. If ΔXYZ has a perimeter of 32 centimeters, what is
the measure of the missing side length in ΔABC ?
27. WHICH ONE DOESN’T BELONG?
Identify the congruent statement that
does not hold true for the figures
shown. Explain your reasoning.
KL RS
28.
702
LM SR
J
K
M
∠K ∠R
Q
L
R
T
∠M ∠T
In this lesson, you learned that two
shapes that are congruent will have the same perimeter. Is it
also true that if two shapes have the same perimeter, then
they are congruent shapes? Explain your reasoning.
S