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ANSWERS
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Game: Hold That Fold
1-1
Game: Points Around the Room
1-2
Nets and Drawings for Visualizing Geometry
Points, Lines, and Planes
Materials
• Scissors
C
B
D
A
Game Play
H
E
• Tape
I
G
Your teacher will divide the class in teams. Cut out the four nets of a cube below. Take a net
and color, shade, or number the faces however you like. Fold the net into a cube and tape
it together. Challenge another team to draw a net of your cube, including any markings or
shadings. If your team accepts the other team’s net, they must cut out its net and fold it up.
If the folded net forms a cube that looks like your team’s cube the other team scores 2 points.
Otherwise, the second team loses 1 point.
Wall
J
F
K
Wall
floor
Ending the Game
Setup
The team with the most points at the end of the game-play period is the winner.
Your teacher will position points around the room, as shown in the figure above.
Game Play
Work in your team to answer the following questions about the points, lines, and
planes your teacher has labeled. If there is more than one answer or more than
one way to write the same answer, record each possibility.
1. What is another name for plane FGK? Samples: plane GJK, FJK, or FGJ or floor
* ) * ) * ) * ) * ) * )
2. What is the intersection of plane ABF and plane HIG? CG , GC , CE , EC , EG , GE
3. What point is collinear with points E and C? G
4. What point is coplanar with points H, E, and C? I, J, G
)
)
5. What is another way to name GE ? GC
)
)
)
6. What two rays are opposite rays? BA and BC , EC and EG
* ) * )
* ) * )
8. What line is coplanar with FG and GJ ?
)
)
7. What is the intersection of GE and AB ? C
)
* ) * ) * )
* )
Samples: KG , FK , JK , or FJ
9. What is the intersection of GE and CE ? GC
10. What point is collinear with A? Any two points are collinear. B, C, D, E, F, G, H, I, J, or K.
Ending the Game
As a class, compile a list of correct answers on the board. For each correct answer, your
team scores a point. This means many points may be possible for some questions. For each
incorrect answer, deduct a point from your score. The team with the most points wins!
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Puzzle: What Is a Line’s Favorite Kind of Fruit?
1-3
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Puzzle: Word Search
1-4
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Measuring Segments
Solve the problems below to answer the
riddle:
Materials
• Protractor
What is a line’s favorite kind of fruit?
Use a protractor and the diagram at the
right to fill in the blanks. Then search the
grid below for the non-numerical answers.
Look for your answer in the key at the right
and put the corresponding letter in the
answer blank at the bottom of the page.
AB 5 4x 2 3, BC 5 7x 1 5, and AC 5 5x 2 16.
Find each value.
a. BC
b. AB
c. AC
2. On a number line, G 5 8 and H 5 23. If H is the midpoint
of GI , find the coordinate of I.
3. J is the midpoint of KL. Find KJ if KL 5 38.
For 4–6, refer to the number line below.
N
O
P
Q
4. Suppose O is the midpoint of MQ and N is the midpoint
of MO. If NO 5 8, find MQ.
5. Suppose P is the midpoint of NQ, OP 5 11, and OQ 5 35.
Find NO.
6. If NO 5 2y 1 11, OP 5 3y 2 2, NP 5 6y 1 3, and
MP 5 64, find each value.
a. NO
b. MN
C
D
B
1. B is in the 9 of /AIC.
1. Points A, B, and C are collinear and A is between B and C.
M
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Measuring Angles
a
b
c
d
e
f
g
h
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j
k
l
m
n
o
p
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r
s
t
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v
w
x
y
z
E
2. m/EID 5 9, so it is a(n) 9 angle. A
–14
20
–18
–13
32
3
23
39
16
41
–11
12
13
89
44
–26
6
19
45
25
42
10
–7
16
27
50
I
3. m/CIH 5 9, so it is a(n) 9 angle.
4. /AIE is a(n) 9 angle.
5. m/BIA 5 9 and m/FIG 5 9,
H
so /BIA and /FIG are 9.
F
G
6. m/AIG 5 9, so it is a(n) 9 angle.
7. The 9 9 Postulate allows you to
say that m/AIB 1 m/AIG 5 m/BIG.
8. A is in the 9 of /DIF .
9. If two angles are congruent, they can be marked with the same number of 9.
An o r a n g e because it is made of s e g m e n t s .
1c 3 2 1a 6a 4
1b 4 6a 5 4 1a 6b 1b
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Prentice Hall Geometry • Activities, Games, and Puzzles
Copyright © by Pearson Education, Inc., or its affiliates. All Rights Reserved.
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ANSWERS
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Activity: Vertical Angles
1-5
* )
Basic Constructions
Materials
• Compass
Use geometry software to do this activity.
Construct
Puzzle: Mystery Pictures
1-6
Exploring Angle Pairs
* )
E
lines AB and AC . Construct point D on
*Construct
)
AB so that A is between D and B. Construct point E
* )
A
D
on AC so that A is between C and E.
B
• Straight edge
Using only a compass and straight edge, follow the directions to construct the
mystery picture.
C
D
1. Find and label C, the midpoint of AB.
Locate
1. a. /
and /
4
b. There are
2. Draw CD such that point D is above C
are adjacent angles. Answers may vary. Sample: EAB, BAC
on the perpendicular bisector of AB
pairs of adjacent angles in the picture.
A
1
and CD 5 2 AB.
2. a. /EAB and / DAC are vertical angles.
B
C
3. Draw CE such that point E is below C
b. /BAC and / EAD are vertical angles.
on the perpendicular bisector of AB
3. a. /EAB and / BAC or EAD are a linear pair.
3
and CE 5 4 AB.
b. So the measures of the angles in part (a) add to 1808 .
4. Draw AD, DB, BE, and AE.
c. This means the angle pair in part (a) can also be called supplementary .
5. Starting at point E, draw a curve
E
through the intersections of each pair
of equilateral triangles.
Investigate
Measure all four angles. Drag points B and C and observe the effect on the angle
measures. /BAC and /EAD are called vertical angles.
Constructions may vary. Sample is given.
1. Construct /RJI such that
4. Make a conjecture about vertical angles. They are congruent.
5. Use ‘Calculate’ to determine the sum of m/EAD and m/EAB. Justify this
result. mlEAD 1 mlEAB 5 1808
m/RJI 5 m/HGF and RJ 5 IJ .
6. Use ‘Calculate’ to determine the sum of m/EAB and m/BAC. Justify this
result. mlEAD 1 mlBAC 5 1808
7. Based on your answers to Exercises 5 and 6, what is the value of the expression
3. Construct /TNM such that
K
the exterior points of /TNM .
Challenge
Design your own mystery picture, and provide directions for its construction.
Check students’ work.
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Game: Cross the Ocean
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Midpoint and Distance in the Coordinate Plane
10
Puzzle: Cross-Number
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Perimeter, Circumference, and Area
Fill in the cross-number puzzle with your answers to the given clues. All
answers should be rounded to the thousandths place when necessary. Each
digit and decimal point of your answer goes in its own box.
y
• Ruler
• Number cube
1
5
2
1
4
4
Your teacher will divide the
class into pairs.
Game Play
G
H
6. Draw an arc with radius NQ through
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Answers may vary.
Samples are shown.
F
the exterior points of /SLK .
11. Challenge Justify the result found in Exercise 10. Answers may vary. Sample:
Adjacent angles are supplementary. The angle bisectors of these angles make a pair
of angles that are complementary.
Setup
x
10
5
Q
P
O
the exterior points of /RJI .
formed by the intersection of two lines. Use the geometry software functions
‘Measure’, ‘Angle’, and ‘Calculate’ to verify this conjecture. They are perpendicular.
Materials
• Graphing calculator
I
5. Draw an arc with radius LP through
10. Make a conjecture about the angle bisectors of the two pairs of vertical angles
1-7
N
L
J
4. Draw an arc with radius JO through
9. Draw two pairs of vertical angles. Construct the angle bisectors of all four
angles formed. Check students’ work.
0005_hsm11gmagp_0105.indd 5
M
R
m/TNM 5 2m/HGF and TN 5 MN .
(m/EAD 1 m/EAB) 2 (m/EAB 1 m/BAC)?
(mlEAD 1 mlEAB) 2 (mlEAB 1 mlBAC) 5 0
8. How does your result in Exercise 7 justify the conjecture made in Exercise 4?
(mlEAD 1 mlEAB) 2 (mlEAB 1 mlBAC) 5 0 simplifies to
mlEAD 2 mlBAC 5 0 which means mlEAD 5 mlBAC
Extend
T
S
2. Construct /SLK such that
3
m/SLK 5 2 m/HGF and SL 5 KL.
O
1
1
3
3
10
3
2
.
.
.
0
9
4
3
8
6
7
.
5
6
8
5
Players choose points on
opposite sides of the board
5
from which to start (left or
right). On your turn, choose
a target point to which you
would like to move, being
certain that your path is
10
straight and does not touch
an “island” in the ocean. Roll the number cube to determine what calculation to
make, using the point you are on and the target point to which you would like to
secure a path.
4
7
.
1
2
4
0
.
2
4
66
2
7
5
6
5
.
0
8
1
8
.
3
3
6
• Roll a 1, 2, or 3: Find the distance between the two points.
• Roll a 4 or 5: Find the midpoint of the segment between the two points.
• Roll a 6: Use your first point as one endpoint and your target point as the
midpoint of a segment. You must find the other endpoint of this segment
that may be on or across an island.
Across
Down
2. perimeter of a triangle with side lengths
1. perimeter of a square with side length
of 13.9 in., 10.4 in., and 8.5 in.
Do your calculations by hand. Your opponent can check your work using a
graphing calculator. If you are correct, use a ruler to draw your path and “move”
to the target point. Note that you always move to the point you selected, not to the
midpoint or endpoint of a segment that you calculated. You may not attempt to
connect two points if your opponent has already done so.
4. area of a circle with a 12-ft diameter
5. circumference of a circle with a 7.5-cm
radius
7. circumference of a circle with a 16-ft
diameter
8. area of a rectangle with dimensions
Ending the Game
4.7 m and 3.9 m
The game ends when one player wins by securing a path from one side of the
board to the other. Check students’ work.
3.6 cm
2. area of a rectangle with dimensions
2.5 in. and 1.5 in.
3. perimeter of a rectangle with dimensions
32.4 m and 10.9 m
4. area of a triangle with a base of 24.5 cm
and height of 11.3 cm
6. area of a square with side length
8.125 cm
Prentice Hall Geometry • Activities, Games, and Puzzles
Copyright © by Pearson Education, Inc., or its affiliates. All Rights Reserved.
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