Name ____________________________________________ Date ____________ Class ____________
Investigation 1
1ACE Exercises 1–6
Looking for Pythagoras
For Exercises 1–6, use the map below.
5 y
N
4
Stadium
Gas station
3
2
1
Greenhouse
᎐7
᎐6
᎐5
᎐4
Art museum
x
City Hall
᎐3
᎐2
᎐1
1
2
3
4
5
6
7
᎐1
᎐2
Animal shelter
᎐3
Hospital
᎐4
Police station
Cemetery
᎐5
a. art museum
b. hospital
c. greenhouse
2. What is the shortest driving distance from the animal shelter
to the stadium?
HINT Remember that a car can drive
only on roads.
3. What is the shortest driving distance from the hospital to the
gas station?
142
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1. Give the coordinates of each landmark.
Name ____________________________________________ Date ____________ Class ____________
Investigation 1
1ACE Exercises 1–6 (continued)
Looking for Pythagoras
4. What are the coordinates (x, y) of a point halfway from City Hall to the
hospital if you travel by taxi?
Is there more than one answer to this question?
Explain.
5. What are the coordinates of a point halfway from City Hall to the
hospital if you travel by helicopter?
HINT How can a helicopter travel
differently than a car? Refer back to
Problem 1.1.
Is there more than one answer to this question?
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Explain.
6. a. Which landmarks on the map are 7 blocks from City Hall by car?
HINT
Check to see if there is more than
one answer to this question.
b. Give precise driving directions from City Hall to each landmark you
listed in part (a).
143
Name ____________________________________________ Date ____________ Class ____________
Investigation 1
1ACE Exercises 8–10
Looking for Pythagoras
The points (0, 0) and (3, 2) are two vertices of a polygon with integer coordinates.
8. What could the other two vertices be if the polygon is a square?
4
y
2
x
–4
–2
2
O
4
–2
–4
9. Suppose the polygon is a non-rectangular parallelogram. What
could the other two vertices be?
4
y
2
x
–4
–2
2
O
4
–4
10. What could the other vertex be if the polygon is a right triangle?
4
y
2
x
–4
–2
O
–2
–4
144
2
4
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–2
Name ____________________________________________ Date ____________ Class ____________
Investigation 2
2ACE Exercise 41
Looking for Pythagoras
41. Put the following set of numbers in order on a number line.
2.3
2 14
4
–2.3
_
√5
_
√2
4
2
–2 14
_
√4
5
2
–
4
2
2.09
HINT Write all the numbers in the same
form, such as all in decimal form, or all in
fraction form.
-2
–2
-1
–1
00
1
1
2
2
33
4
4
55
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-3
–3
145
Name ____________________________________________ Date ____________ Class ____________
Investigation 3
3ACE Exercises 8–11
Looking for Pythagoras
For Exercises 8–11, use the map. Find the flying distance in blocks between the
2 landmarks without using a ruler.
5 y
N
4
Stadium
Gas station
3
2
1
Greenhouse
᎐7
᎐6
᎐5
᎐4
Art museum
x
City Hall
᎐3
᎐2
᎐1
1
2
3
4
5
6
7
᎐1
᎐2
Animal shelter
᎐3
Hospital
᎐4
Police station
Cemetery
8. Greenhouse and stadium
flying distance:
Explain how you found this answer.
146
Remember what flying distance
refers to. It is not the same as the driving
distance. Look it up if you do not
remember.
HINT
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᎐5
Name ____________________________________________ Date ____________ Class ____________
3ACE Exercises 8–11 (continued)
Investigation 3
Looking for Pythagoras
9. Police station and art museum
flying distance:
Explain how you found this answer.
10. Greenhouse and hospital
flying distance:
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Explain how you found this answer.
11. City Hall and gas station
flying distance:
Explain how you found this answer.
147
Name ____________________________________________ Date ____________ Class ____________
Investigation 4
4ACE Exercise 8
Looking for Pythagoras
8. The diagram shows an amusement park ride in which tram cars glide along a
cable. How long, to the nearest tenth of a meter, is the cable for the ride?
HINT
The picture is not drawn to scale.
Not drawn to scale
15 m
15 m
45º
45º
1,000 m
HINT Divide the ride into parts. There is
a part where the ride slopes up, a part
where the ride is level (most of the ride),
and a part where the ride slopes down.
HINT Use what you have learned about
right triangles and the lengths of their sides
to figure out the lengths of the parts of the
ride that slope up and down.
How long is the part of the ride that slopes down?
How long is the part of the ride that is level?
How long, to the nearest tenth of a meter, is the cable for the ride?
148
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How long is the part of the ride that slopes up?
Name ____________________________________________ Date ____________ Class ____________
Partner Quiz
Looking for Pythagoras
1. The three line segments are drawn on centimeter dot paper.
a. Find the length of each segment to the nearest
ten-thousandth of a centimeter.
b. Could these line segments be arranged to form a triangle?
If no, explain why not.
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If yes, answer this question: Could they form a right triangle?
Explain your reasoning.
2. Use the diagram below to answer parts (a)–(f). Show all the work
you do to find your solutions.
B
A
C
D
a. What is the area of square ABCD?
149
Name ____________________________________________ Date ____________ Class ____________
Partner Quiz (continued)
Looking for Pythagoras
b. What is the length of line segment AB?
c. What is the distance from A to C?
d. What is the area of triangle ABC?
f. Explain how the perimeter of square ABCD compares to the
perimeter of triangle ABC.
150
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e. Explain how the area of square ABCD compares to the area of
triangle ABC.
Name ____________________________________________ Date ____________ Class ____________
Investigation 1
Partner Quiz (continued)
Looking for Pythagoras
3. The gardener wants to brace the gate on the left below by adding a diagonal
strip of wood between the two horizontal strips (as shown on the right).
3 ft
HINT The section of gate at the
left is the same as the section of gate
on the right. The section of gate on
the right (with the diagonal strip of
wood) is what the gardener wants
the gate to look like.
5 ft
© Pearson Education, Inc., publishing as Pearson Prentice Hall. All rights reserved.
a. How long should the diagonal strip of wood be? (Do not worry about
trimming the ends to make a perfect fit.) Show all the work you do to find
your solution.
HINT Think about what you know. You
know the length of the two boards (5 ft)
and the distance between them (3 ft). How
can you find the length of the diagonal?
b. A standard tape measure is marked in feet and inches. If your answer for
part (a) is written only in feet, rewrite it in feet and inches.
What is your answer from part (a)?
How many feet are in your answer?
How many inches are in your answer?
HINT There are 12 inches in 1 foot. The
decimal places that follow a whole number
are out of 10, so you need to figure out
how many inches are represented by the
decimal number.
For example, if the answer is 4.6, that is
4 feet and some inches. To find the
number of inches, figure out how many
6
x
inches 0.6 is. That means 10
= 12
.
Multiply 6 ⫻ 12 to get 72. Then divide 72
by 10 to get 7.2. So the answer is 4 feet
and 7.2 inches.
151