Geometry: Constructing Triangles and
Scale Drawings – AP Book 7.1: Unit 6
AP Book G7-1
2.
page 152
1.
2.
3.
4.
a)
a)
Picture B
b)
Picture A incorrectly
lined up the base line
and incorrectly
placed the origin.
ray
b)
line
c)
line segment
Picture C incorrectly
lined up the base
line.
The following points should
be circled.
a)
A
b)
43°
b)
A and C
c)
130°
c)
D
d)
127°
a)
yes
e)
105°
b)
yes
f)
55°
c)
yes
a)
C lines up with 60°
d)
no
b)
A lines up with 140°
a)
ii)
3.
4.
4.
5.
6.
5.
Teacher to check.
6.
Teacher to check.
7.
Teacher to check.
d)
less than
a)
no
b)
yes
b)
c)
yes
d)
no
a)
No because they are
not the same size.
b)
Yes because they
are the same size
and the same shape.
a)
3
b)
5
2.
a)
i)
ii)
iii)
iii)
AP Book G7-3
page 157
1.
a)
ii) getting closer
together
3.
c)
iii) getting closer
together
5.
b)
the arms in part iii)
iv) neither
b)
40°
c)
70°
v) getting farther
apart
Bonus
d)
6.
7.
e)
50°
f)
30°
c)
right
d)
obtuse
e)
right
f)
acute
a)
acute
b)
right
c)
acute
d)
obtuse
e)
acute
f)
obtuse
b)
page 154
1.
obtuse so 150°
c)
acute so 60°
d)
obtuse so 140°
K-30
9
b)
4.
b)
5.
yes
7.
yes
8.
a)
congruent
b)
congruent
no
180°
iii)
yes
150°
Triangle? Sum of
Angles
i)
no
180°
ii)
no
200°
iii)
yes
150°
less than
b)
greater than
c)
exactly
i)
B
no
Placement of triangle may
vary.
Teacher to check.
Sample answers:
a)
150°
ii)
b)
90°
ii) A
Triangle? Sum of
Angles
i)
a)
a)
less than
a)
i)
ii) 90°
less than
3.
b)
d)
equal to
AP Book G7-2
i)
ii)
greater than
2.
a)
1
vi) getting farther
apart
20°
Half of 90° is 45°.
Teacher to check.
AP Book G7-4
page 159
1.
b)
Answers may vary.
Teacher to check.
Sample answers:
a)
6.
Teacher to check.
Answer Keys for AP Book 7.1
COPYRIGHT © 2015 JUMP MATH: NOT TO BE COPIED. CC EDITION
iv)
b)
c)
Geometry: Constructing Triangles and
Scale Drawings – AP Book 7.1: Unit 6
AP Book G7-5
page 161
1.
b)
yes
3.
a)
yes
COPYRIGHT © 2015 JUMP MATH: NOT TO BE COPIED. CC EDITION
b)
no
Longest
c)
yes
Shortest
Side
d)
yes
e)
yes
9
6
f)
no
16
15
g)
yes
c)
5
4
a)
Teacher to check.
d)
7
5
b)
Teacher to check.
e)
8
7
c)
no
f)
9
8
d)
Teacher to check.
e)
Teacher to check.
2, 2, 4
3, 5, 7
2, 5, 6
4
8
7
4
7
6
no
yes
yes
5.
9
1
yes
no
no
Teacher to check.
b)
The third angle is 60°
in all the triangles.
c)
no
a)
ii) 180°
e)
5.

g)

h)

i)

l)
6.
no
9 − 5 = 4, so the sum of the
shortest two sides can only
be 4 inches and that does
not add to more than the
longest side of 5 inches.
AP Book G7-7
yes
2 feet = 24 inches. The
sum of the shortest two
sides is 11 + 14 = 25,
which is more than the
longest side.
1.
2.
AP Book G7-6
page 163
3.
90°
Answer Keys for AP Book 7.1
a)
The third square
should be circled.
b)
The second circle
should be circled.
a)
B
b)
D
c)
E
d)
C
a)
circle kite
b)
10
c)
9×5
A = 3 cm
2 cm
A = 4 cm
2
P = 8 cm
8.
a)
4 squares: B, C, D,
E, F, G
5 squares: A, H, I, J
b)
c)
A and I,
B and F,
C and D,
E and G,
H and J.
Statement B is true.
Step 1: boat, bat,
bait, and bee should
be circled.
Statement A is false.
Sample
counterexample:
Step 2: bee
B and C
9.
a)
b)
A number that is
even that is not a
multiple of 4.
c)
A product of two
numbers that is a
multiple of 9, where
one number is not a
multiple of 3.
Statement A is true
because 45° + 45°
= 90°. Since the
angles in a triangle
always add to 180°,
the remaining angle
must be 90°.
Statement B is false.
Sample
counterexample:
A triangle with a 90°
angle and the other
two angles are 30°
and 60°.
Step 1: 1, 2, 3, 4, 6,
8, 12, and 24.
Step 2: 3, 6, 12, and
24 are possible
counterexamples.
6.
2
P = 8 cm
Step 2: C
d)
rhombus
Bonus
The third, fifth, and
seventh flags should
be circled.
Step 1: B, C and D
pairs should be
circled.
page 165
Bonus
a)
The second figure
(spotted triangle) and
the third figure
(shaded rectangle)
should be circled.
c)

m)
Answers will vary.
Sample answers:
Step 2: soccer

k)
The first (unshaded
square), third
(shaded pentagon),
and fourth (shaded
circle) figures should
be circled.
Step 1: mice, cedar,
face, soccer, and
voice should be
circled.

j)
7.
The second figure
(shaded square) and
the fourth figure
(shaded triangle)
should be circled.
b)
Bonus
180°
Teacher to check.
a)

f)
iii) 180°
a)
No

e)
The sum of the shortest
two sides is 2 + 4 = 6,
which is less than 7, so it
does not make a triangle.
a)
The third figure
(unshaded circle)
should be circled.

d)
23
24
4
More

c)
a)
d)

b)
Bonus
4, 4, 9 1 , 5 , 1
3 8
8
Unique
circle Sam
c)
b)
4.
b)
b)
a)
b)
1.
no
Sum of Two
7
7.
4.
Teacher to check.
3, 4, 4
6.
no
2.
Sides
5.
c)
yes
2.
4.
Teacher to check.
a)
c)
3.
b)
(continued)
b)
Statement B is true
because 3 is already
less than 5.
Statement A is false.
Sample
counterexample: 4
Bonus
A shape that has a
smaller area than
another shape that
does not also have a
smaller perimeter.
K-31
Geometry: Constructing Triangles and
Scale Drawings – AP Book 7.1: Unit 6
Statement B is true
because triangles
that are congruent
have the same three
angles.
Statement A is false.
Sample
counterexample:
Two triangles could
have the same three
angles, but be
different sizes.
d)
Statement A is true
because triangles
that are congruent
have the same side
lengths and,
therefore, the same
perimeter.
6.
7.
2.
a)
Teacher to check
that the triangle is
6 units tall and
8 units long.
ii) yes
5.
1.
Teacher to check.
2.
a)
Scale
Drawing
(mm)
15
30
20
40
25
50
b)
3.
Original
Length
(mm)
Scale
Drawing
(mm)
9
27
16
48
9
6
b)
4.
6.
a)
b)
Length
Width
5
2
4
1.6
Original
Room is 4 squares
long and 3 squares
wide.
b)
Room is 8 squares
long and 6 squares
wide.
c)
Room is 12 squares
long and 9 squares
wide.
a)
Closet is 3 squares
long and 2 squares
wide.
b)
Closet is 9 squares
long and 6 squares
wide.
Bonus
1:6
5.
Scale
5
4
2
1.6
a)
page 173
ii)
Scale Drawing
(grid squares)
iii)
1.
Teacher to check.
Scale Drawing
(grid squares)
6
3.
2
K-32
4.
20 8 4
= =
15 6 3
AP Book G7-10
C. 1 : 4
Dimensions in clockwise
order from given side
length: 6 in, 8 in, 8 in, 2 in,
2 in, 14 in, 4 in.
a)
12 9 3
= =
8
6 2
ii)
B. 1 : 3
5.
i)
yes
A. 1 : 2
92 mm
2
5
b) The unit ratio is 1 : 3.
2
c)
3.
6
a)
18 ft
b)
12 ft
c)
i)
a) The unit ratio is 1 : 2.
B. 2 : 6
36 mm
240 − 114
= 126 inches of
countertop space left
in the kitchen.
Scale
Yes, because the rows in
the tables are equivalent
ratios.
5
20 mm
3
4
yes
A. 2 : 4
b)
i)
8
Original
Length
(mm)
a)
a)
a)
12 grid squares
= 240 inches
30 + 28 + 24 + 32
= 114
iii) yes
C. 1 : 4
4.
f)
Scale
yes
c)
yes
page 170
b)
b)
i)
AP Book G7-9
page 168
1.
It is not a scale drawing
because, when making a
new drawing, you must
multiply every length and
width by the same number,
not add to it.
d)
ii)
Statement B is false.
Sample
counterexample:
A 2 cm by 3 cm
rectangle has the
same perimeter as a
4 cm by 1 cm
rectangle.
AP Book G7-8
Shapes A and C are similar
because each side in
Shape C is twice the length
of each side in Shape A.
b)
c)
iii)
30 : 12
15 : 5
5:2
6:2
ii)
iii)
5:2
3:1
5:2
3:1
ii) Room is
9 squares long
and 6 squares
wide.
On Map
(mm)
Real Life
(mi)
a)
19
950
b)
14
700
c)
35
1,750
iii) Room is
12 squares long
and 8 squares
wide.
d)
28
1,400
Bonus
e)
49
2,450
f)
24
1,200
Floor Plan
Real Life
(grid squares)
(inches)
a)
4
80
b)
4
80
c)
5 by 3
100 by 60
d)
4
80
e)
3
60
2.
ii)
Room is
3 squares long
and 2 squares
wide.
Room is
4.5 squares long
and 3 squares
wide.
6.
scale is
1
in : 1 mile.
4
1 grid square =
1
mi.
4
Answer Keys for AP Book 7.1
COPYRIGHT © 2015 JUMP MATH: NOT TO BE COPIED. CC EDITION
c)
(continued)
Geometry: Constructing Triangles and
Scale Drawings – AP Book 7.1: Unit 6
7.
(continued)
Actual height = 3 ft
Actual width = 5 ft
New picture height
= 1.5 cm
New picture width
= 2.5 cm
30 ft
COPYRIGHT © 2015 JUMP MATH: NOT TO BE COPIED. CC EDITION
8.
Answer Keys for AP Book 7.1
K-33