Download Geometry: 2-D Shapes – AP Book 5.2: Unit 7

Geometry: 2-D Shapes – AP Book 5.2: Unit 7
AP Book G5-6
page 144
1.
a)
b)
c)
line segment
2 endpoints
line
0 endpoints
ray
1 endpoint
2.
Teacher to check.
3.
Teacher to check.
4.
Teacher to check.
5.
a)
Left
b)
Left
c)
Left
d)
Left
a)
Same
b)
Not the same
a)
Left
b)
Left
a)
Greater
b)
Less
c)
Greater
d)
Greater
6.
7.
8.
7.
8.
b)
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3.
1.
2.
3.
4.
3 sides
3 vertices
a)
Teacher to check.
b)
No
b)
30 degrees
c)
80 degrees
b)
more than 90
c)
less than 90
d)
more than 90
e)
more than 90
f)
less than 90
a)
acute
b)
obtuse
c)
obtuse
d)
obtuse
e)
acute
f)
acute
a)
acute
b)
obtuse
c)
acute
d)
obtuse
e)
obtuse
f)
acute
b)
d)
5 sides
5 vertices
acute
30
c)
e)
6 sides
6 vertices
obtuse
120
d)
f)
8 sides
8 vertices
obtuse
150
a)
g)
8 sides
8 vertices
acute
50
b)
acute
30
5.
6.
11 sides
11 vertices
c)
C
It is not a polygon
because not all sides are
line segments.
b)
6 sides
hexagon
c)
3 sides
triangle
5 sides
pentagon
Triangle: A, H
Quadrilateral: B, G, I
Pentagon: C, F
Hexagon: D, E
Other: J
5.
Other
6.
Teacher to check.
Answer Keys for AP Book 5.2
No.
6 sides
6 vertices
d)
4.
b)
c)
BONUS
2.
The number of sides
is equal to the
number of vertices.
AP Book G5-9
page 151
7.
8.
obtuse
115
d)
acute
45
e)
obtuse
153
Teacher to check.
a)
90 35 55
b)
65 75 40
3.
a)
108
b)
118
c)
120
4.
Teacher to check.
Teacher to check.
1.
b)
C, D, E
c)
A, C, D, F
2
7
1
3
3
b)
Teacher to check.
c)
Teacher to check.
d)
No, because numbers
cannot be both odd and
even.
5.
a)
B
C
b)
AP Book G5-10
page 153
F
A
D
E
BDF
A
E
C
2.
a)
6.
B
H
C
D
b)
A
E
C
D
B
F
G
AP Book G5-11
page 155
3.
a)
B
1.
E
C
D
A
F
2
b)
B
i)
b)
The baseline is not
lined up with one
arm of the angle.
58
A
7.
4. a)
130
b)
6.
B
b)
52
C
Teacher to check.
a)
c)
d)
a)
5.
obtuse
105
30
12
2.
f)
a)
ii)
1.
AP Book G5-8
page 148
AP Book G5-7
page 146
1.
a)
E
A
C
D
F
3.
4.
1
2 3
12
3
a)
30mm, 30 mm,
25 mm, 25 mm
b)
20 mm, 21 mm,
21 mm, 27 mm
a)
27 mm
b)
20 mm
c)
40 mm, 20 mm
d)
22 mm
a)
60
b)
90
c)
120
d)
95, 85
a)
Teacher to check:
A, B, G
b)
All angles equal:
A, B, C, G
7
Equilateral:
A, B, E, F, G
DH
c)
E
F
A
B
G
C
T-19
Geometry: 2-D Shapes – AP Book 5.2: Unit 7
(continued)
The overlap.
e)
Teacher to check.
iv)
2.
3.
4.
a)
90
52
b)
20
118
42
Teacher to check.
b)
acute
c)
right
d)
obtuse
a)
acute
b)
right
c)
acute
d)
obtuse
F
A
D
AP Book G5-12
page 157
1.
EG
10.
Teacher to check.
a)
Acute
b)
No, because all
three angles of a
triangle must add up
to 180 so no two
angles can be 90,
nor can two angles
be obtuse in the
same triangle.
6.
All three angles in an
acute triangle are acute.
1.
Teacher to check.
a)
2.
a)
8.
isosceles
b)
equilateral
b)
Yes
isosceles
c)
No
d)
scalene
d)
Yes
a)
i) scalene
e)
Yes
ii) isosceles
f)
Yes
iii) equilateral
g)
Yes
h)
No
iv) isosceles
b)
i) right-angle
3.
Teacher to check.
ii) right-angle
4.
Teacher to check.
iii) acute
5.
Teacher to check.
iv) acute
9.
6.
a)
Teacher to check.
b)
Acute: A, D, F
a)
Right: C, G
Obtuse: B, E
Equilateral: D
Isosceles: A, E, G
Scalene: B, C, F
c)
i)
7.
BCE
G
A
F
B
iii)
G
A
E
Teacher to check
drawings.
a)
Teacher to check.
b)
90
c)
Teacher to check,
answers may vary.
d)
You can use right
angles to draw
parallel lines
because they can
check to see if a
perpendicular line is
crossing two parallel
lines.
CD
F
C
1.
BF
2.
a)
a)
parallelogram
b)
trapezoid
trapezoid
Trapezoids have
only 1 pair of
parallel sides, while
parallelograms have
2 pairs. A
quadrilateral cannot
be both.
ii) 108, 72
108, 72
iii) 90 90 90 90
Opposite angles of
a parallelogram are
equal.
c)
No.
4.
P, P, T, T, P
5.
a)
Teacher to check.
b)
Circle i), ii), and v)
c)
Parallelograms
L: 50 mm, 21 mm
d)
No, opposite angles
are not equal.
N: 32 mm, 23 mm
b)
b)
K: 39 mm, 19 mm
M: 25 mm, 35 mm
Parallelograms:
K, N
Trapezoids:
L, M
Parallel sides equal:
K, N
Parallel sides not
equal:
L, M
c)
Parallelograms have
equal length parallel
sides, whereas
trapezoids do not.
d)
i) 60 mm, 56 mm
Other pair not
parallel, a trapezoid
6.
Teacher to check.
AP Book G5-16
page 166
1.
Teacher to check.
Circle a, b, e.
2.
a)
Yes
b)
No
3.
a)
Right-angled
b)
They would not be
right-angled
triangles.
c)
Teacher to check.
4.
Teacher to check.
5.
b)
ii) 40 mm, 40 mm
Other pair parallel,
parallelogram
5.
E
D
Ron is incorrect because
equal opposite side
lengths does not mean
that the sides are parallel.
Also, the two sides that
are parallel are not of
equal length. It is a
trapezoid.
1.
a)
C, G
b)
Teacher to check.
c)
None
B, D
2
A
3
E, I
4
F
2 pairs
d)
2.
C, G, H
6.
C
F
A
c)
C, F
d)
In the overlap
section
d)
Diagonals of a
rectangle are equal
length and not
perpendicular,
which is not the
same for other
parallelograms
a)
Teacher to check;
explanations may
vary.
Sample answer:
All rectangles are
also parallelograms
because rectangles
have two pairs of
equal length,
parallel sides.
AP Book G5-15
page 164
Teacher to check.
c)
T-20
4.
AP Book G5-14
page 162
ADE
G
Teacher to check
drawings.
i) 2
ii) 3
iii) 0
BONUS 2
b)
D
ii)
b)
No
a) i) 120, 60
120, 60
A
C
G
D F
No
c)
3.
B
E
H
AP Book G5-13
page 160
Teacher to check.
b)
parallelogram
a)
B
C
d)
5.
7.
d)
3.
4 or 2 pairs
e)
2
a)
Yes
Answer Keys for AP Book 5.2
COPYRIGHT © 2013 JUMP MATH: NOT TO BE COPIED. CC EDITION
d)
Geometry: 2-D Shapes – AP Book 5.2: Unit 7
(continued)
Teacher to check;
explanations may
vary. Sample
answer: The length
of the other two
sides are 6 cm and
15 cm because a
rectangle is also a
parallelogram, and
they have equal
length opposite
sides.
b)
7.
4.
All angles in a
quadrilateral add up
to 360, so with
three exact angles
at 90, the fourth
angle must also be
90.
b)
Teacher to check.
Sample answer:
Any parallelogram
that has at least 2
right angles has to
be a rectangle
because of the
number of degrees
needed to add up to
the required 360.
BONUS
They are
perpendicular.
a)
Yes, as squares are
two sets of parallel
lines.
b)
Yes, as all four
sides of a square
are equal, as in a
rhombus, and there
are two sets of
parallel lines.
c)
Yes, because
angles in a
quadrilateral add up
to 360. All
quadrilaterals with 4
equal angles will
have 90, making it
a rectangle.
a)
e)
No, as a trapezoid
does not have equal
length sides, and
only has one set of
parallel lines.
d)
Overlap section
e)
No, as a polygon
that is a rhombus
and also rectangle
must also be a
square.
b)
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2.
3.
A
B
S?
3
3
Y
0
0
Y
0
1
N
3
2
N
2
0
N
C
D
S?
4
4
Y
2
2
Y
4
0
N
2
2
Y
2
2
Y
b)
i) rhombus
ii) no
iii) rhombus
a)
Yes
a)
Teacher to check.
Teacher to check.
E
F
S?
c)
Different
6
5
N
d)
Teacher to check.
6
5
N
e)
Teacher to check.
3
0
N
f)
C
a)
Teacher to check.
N
b)
B
C
D
Teacher to check.
a)
No, because the
sides are not of
equal length.
b)
Teacher to check.
4.
a)
Square
b)
Rhombus
c)
Right-angled
isosceles triangle
AP Book G5-19
page 172
1.
Teacher to check.
2.
Teacher to check.
3.
a)
Quadrilateral
Parallelogram
b)
Quadrilateral
Parallelogram
Rhombus
c)
Quadrilateral
Parallelogram
Rhombus
Square
Rectangle
d)
Quadrilateral
Parallelogram
Rectangle
4.
Teacher to check.
c)
b)
A
E
F
b)
3.
a)
AP Book G5-17
page 168
1.
a)
AP Book G5-18
page 170
1.
A: Parallelogram
B: Rhombus
C: Rectangle
D: Square
E: Trapezoid
F: Trapezoid
2.
2
0
Y
Y
Y
N
Y
N
d)
Teacher to check
drawings.
No.
e)
Teacher to check.
BONUS
c)
B, C, D
d)
In the overlap
section
Answer Keys for AP Book 5.2
Teacher to check.
BONUS
Teacher to check.
T-21