Download Geometry 1 – AP Book 4.1

page 1
Geometry 1 – AP Book 4.1
AP Book G4-1
page 148
6.
1.
7.
a)
4 sides
4 vertices
b)
3 sides
3 vertices
c)
4 sides
4 vertices
d)
5 sides
5 vertices
e)
6 sides
6 vertices
f)
g)
8.
2.
4.
× ×
AP Book G4-3
page 152
Answers may vary by a
few degrees.
AP Book G4-2
page 150
2.
Teacher to check
a)
3.
Teacher to check
b)
30°
1.
4.
Teacher to check
c)
129°
3 sides
3 vertices
8 sides
8 vertices
less than
b)
greater than
d)
124°
c)
greater than
104°
d)
greater than
AP Book G4-4
page 153
e)
f)
57°
e)
less than
1.
f)
greater than
b)
greater than 90°
g)
greater than
c)
less than 90°
h)
greater than
d)
greater than 90°
AP Book G4-5
page 156
e)
greater than 90°
1.
2.
The angles in (b) and (d)
are right angles.
3.
Teacher to check.
k)
8 sides
8 vertices
4.
l)
8 sides
8 vertices
5.
a)
2.
12 sides
12 vertices
2 curved sides
2 straight sides
b)
b)
4 sides
c)
5 sides
d)
6 sides
a)
3
b)
4
c)
4
d)
3
a)
d)
3.
Triangles
A, D
Shapes
Letters
Triangles
A
Quadrilaterals B, F,G
Pentagons
C, D
Hexagons
E, H
6.
7.
Answers will vary.
a)
N
less than 90°
b)
Y
greater than 90°
c)
N
h)
less than 90°
d)
Y
i)
greater than 90°
e)
Y
a)
less than 90°
 60°
f)
Y
g)
Y
b)
greater than 90°
 120°
h)
N
c)
less than 90°
 30°
d)
greater than 90°
 150°
a)
less than 90°
 60°
b)
less than 90°
 40°
c)
greater than 90°
 120°
d)
less than 90°
 30°
e)
greater than 90°
 140°
greater than 90°
 110°
f)
Letters
5.
g)
e)
Shapes
less than 90°
f)
No right angles
c)
4 curved sides
4 straight sides
3 sides
43°
a)
10 sides
10 vertices
a)
In the angles provided,
some of the lines are too
short to be measured by
a standard protractor.
Please show your
students how to use a
ruler to extend the lines
if necessary.
b) and d) are half right
angles
j)
a)
4.
1.
8 sides
8 vertices
Quadrilaterals B, C
5.
23 sides
12 sides
12 vertices
b)
3.
Answers will vary but, no,
you can’t draw a polygon
in which the number of
sides does not equal the
number of vertices.
i)
m)
A
8.
b) Answers will vary
BONUS:
h)
a) Answers will vary.
a)
Answers will vary.
f)
b)
B, E, H and I each
have 4 right angles
g)
a)
Answers will vary.
less than 90°
 45°
b)
K and R have both
a right angle and
an acute angle.
h)
greater than 90°
 135°
BONUS:
Answers will vary
2.
Teacher to check.
3.
Teacher to check – in all
cases, the original lines
will still be parallel.
4.
b)
×
×
×
c)
×
d)
e)
×
×
×
×
Answer Key for AP Book 4.1
page 2
Geometry 1 – AP Book 4.1 (continued)
f)
b)
×
×
×
5.
a)
1 pair
b)
2 pairs
c)
1 pair
d)
2 pairs
4.
AP Book G4-6
page 158
1.
Property
a)
A, B, D, E, F, G
5.
b)
A, E, G
a)
c)
A, C, G, H,
K
left and right: 2 cm
a)
Each side of the
pentagon is 2 cm –
should be circled
c)
The two horizontal
sides of the rectangle
are 4 cm, and the
two vertical sides are
1 cm – not equilateral
b)
3.
4.
Equilateral
B, G, H, J
d)
4 sides
e)
5 sides
Not
Equilateral
A, C, D, E,
F, I
f)
F (not equilateral)
g)
Answers will vary.
Property
A, B, F, H, J
AP Book G4-7
page 159
1 right
I
2 right
1.
4 right
a)
b)
parallelogram
c)
square
d)
rhombus
a)
4 right angles;
rectangle
b)
4 right angles; square
c)
0 right angles
parallelogram
Rhombus:
A parallelogram with
4 equal sides
5.
a)
2 pairs – rectangle
D, E
b)
1 pair – trapezoid
C, G
c)
2 pairs –
parallelogram
Property
Shape
6
No parallel
lines
B, I, J
7.
Answers will vary.
E - 0 pairs
8.
a)
F - 2 pairs
1 pair
D, E
b)
no
G - 1 pair
2 pairs
C, F, G, H
c)
no
3 pairs
A
d)
some
C - 1 pair
c)
D - 2 pairs
H - 2 pairs
None
1 pair
E
C, G
A, B, D,
F, H
3.
a)
9.
2 pairs
d)
Shape
10. square or rhombus
11. Answers should include
three of the following:
Pentagon
D, E, J
No right
B, G, I, K
Hexagon
A
1 right
J
2 right
D, E, F
4 right
A, C, H
Differences:
A parallelogram has
2 pairs of parallel
sides; a trapezoid
has only 1 pair.
AP Book G4-9
page 163
1.
2.
a)
4, 6
b)
1, 2, 3, 5, 7
c)
4, 6
a)
b)
c)
d)
e)
square or rectangle
B, I
Quadrilateral C, F, G, H
Similarities:
Both have 4 sides;
both have at least 1
pair of parallel sides.
all
Triangle
Shape
c)
Answers will vary.
Name
Property
Similarities:
Both have 4 equal
sides.
Differences:
A square contains
4 right angles.
Square:
A parallelogram with
4 right angles and
4 equal sides
B - 2 pairs
2.
rectangle
Rectangle:
A parallelogram with
4 right angles
Shape
No right
b)
Shape – rhombus
2.
Similarities:
Both have 2 pairs of
parallel sides.
Differences:
A rhombus has
4 equal sides.
0 right angles
all sides: 2 cm
Each side of the
rhombus is 1.5 cm –
should be circled
C
12. a)
Shape – rectangle
Each side of the
triangle is 2.5 cm –
should be circled
b)
rhombus – since it’s a
parallelogram with 4 equal
sides.
4 right angles
2 pairs
Shape
A - 2 pairs
a)
top and bottom: 3 cm
Property
b)
1.
D, E, F, I
d)
NonB, D, F, H, I,
Quadrilateral K
AP Book G4-8
page 161
1 pair
Shape
Quadrilateral A, C, E, G,
J, L
2.
Shape
No parallel B, J
lines
×
g)
Property
3.
Answers will vary.
quadrilateral – since it has
4 sides;
AP Book G4-10
page 164
parallelogram – since it has
2 pairs of parallel sides;
1.
rectangle – since it’s a
parallelogram with 4 right
angles;
2.
a)
not congruent
b)
congruent
c)
not congruent
a)
2 and 3
b)
1 and 3
nd
st
rd
rd
Answer Key for AP Book 4.1
page 3
Geometry 1 – AP Book 4.1 (continued)
c)
3.
4.
nd
rd
st
nd
Rectangle  2
st
rd
Rhombus  0
st
nd
st
rd
2 and 3
d)
1 and 2
e)
1 and 3
f)
1 and 2
g)
1 and 3
h)
2 and 4
nd
th
st
rd
i)
1 and 3
j)
2 and 3
nd
rd
From left to right –
A; B; shape not congruent
to others; B; A; shape not
congruent to others
Square  4
c)
Teacher to check.
2.
Teacher to check.
Teacher to check.
3.
Two A’s:
Figure
T
S
P
H
1.
Teacher to check.
# Edges
3
4
5
6
2.
Teacher to check.
# L of S
3
4
5
6
3.
a)
b)
b)
If a polygon is
regular, the number
of edges it has will
equal the number of
lines of symmetry
it has.
4.
AP Book G4-14
page 168
a)
1.
a)
a)
Two D’s:
6.
b)
Example:
2 lines of symmetry:
B
Yes, because they
are the same size
and shape (colour
doesn’t matter)
c)
2 lines of symmetry
3.
No, because they are
not the same shape
d)
a)
b)
e)
Answers will vary.
H, I, O and X all
have two lines of
symmetry.
a)
BATH
b)
BED
c)
MAD
Midpoint – 2.25cm
b)
Line width: 4.4 cm
Midpoint – 2.2 cm
Teacher to check.
a)
a)
Answers will vary.
b)
Teacher to check lines
of symmetry drawn on
page.
F1 F2 S? D?
# vertices
3
3
√
# edges
3
3
√
# of parallel
sides
0
0
√
# of right
angles
0
1
√
lines of
symmetry?
Y
N
√
# of lines of
symmetry
1
0
√
equilateral?
N
N
Property
S? D?
# vertices
√
# edges
√
# of parallel
sides
√
√
AP Book G4-15
page 169
lines of
symmetry?
√
1.
# of lines of
symmetry
√
a)
A. 31, 31, 31 mm
Equilateral
B. 37, 37, 52 mm
Isosceles
√
b)
# of right
angles
no lines of symmetry
AP Book G4-13
page 167
1.
a)
b)
1 line of symmetry:
4.
or
Line width: 4.5 cm
1.
Answers may vary.
D
Teacher to check.
a)
Teacher to check.
A
2.
** remaining shapes aren’t
congruent with anything
b)
2.
Example:
Two C’s:
a)
Scalene
AP Book G4-16
page 170
1 line of symmetry:
Triangles
Isosceles B, C, E, F
Property
5.
5.
Property
Equilateral A
3.
Three B’s:
Teacher to check.
b)
a)
b)
4.
F. 29, 26, 26
Isosceles
Teacher to check lines of
symmetry drawn on page.
AP Book G4-12
page 166
AP Book G4-11
page 165
2.
E. 25, 35, 35
Isosceles
Parallelogram  0
7.
Teacher to check.
1.
D. 50, 33, 68
Scalene
equilateral?
2.
√
Answers will vary.
C. 67, 40, 40
Isosceles
Answer Key for AP Book 4.1
page 4
Geometry 1 – AP Book 4.1 (continued)
F1 F2 S? D?
Property
a)
b)
c)
# vertices
5
5
√
# vertices
4
3
6
# edges
5
5
√
# edges
4
3
6
# of parallel
sides
1
0
3
# of right
angles
0
1
0
lines of
symmetry?
Y
N
Y
# of lines of
symmetry
1
0
6
equilateral?
N
** but F1 has
all straight
sides and F2
includes a
curved side!
# of parallel
sides
0
1
√
# of right
angles
0
0
√
lines of
symmetry?
Y
Y
√
# of lines of
symmetry
5
1
√
equilateral?
Y
N
√
a)
A
F
C
D
H
E
G
B
b)
Property 1: C, D, H
Property 2: B, C, F, H
C & H have both
properties:
A
N
Y
N
N
B
N
N
N
Y
C
Y
N
Y
N
D
Y
Y
Y
Y
2.
N
a)
4
b)
b)
F - 3 vertices
6.
Both shapes have two
parallel sides
Teacher to check.
All four sides are not
always equal
c)
Only 2 sides are
parallel – there are
no 2 pairs of parallel
sides.
# of parallel
sides
0
2
√
# of right
angles
0
4
lines of
symmetry?
Y
Y
# of lines of
symmetry
1
4
√
equilateral?
N
Y
√
T - equilateral
c)
√
T - quadrilateral
F - 2 pairs of
parallel sides
F - at least one
right angle
√
d)
F - 6 vertices
T - no right angles
a)
T - at least 2 pairs of
parallel sides
Parallelogram or
rhombus
F1 F2 S? D?
3.
b)
rectangle
a)
equilateral triangle
c)
trapezoid
rhombus
parallelogram
4
√
4
√
c)
# of parallel
sides
1
1
√
2
0
Property 2: D, E, G, H
# of right
angles
D, E & H have both
properties:
lines of
symmetry?
N
Y
√
# of lines of
symmetry
0
1
√
equilateral?
N
N
B
T - 4 vertices
b)
√
4
F
N
Because all four
angles are right
angles.
4
4
G
Teacher to check.
Example:
a)
3
# edges
D
H
E
a)
Example answers:
# vertices
C
A
5.
T - no right angles
F
Property 1: A, C, D,
E, H
A & H. D & E and B & G;
each pair is the same size
and shape
F - 5 sides
B
G
4.
T - at least 2 right
angles
b)
C
H
E: 1 name (trapezoid)
√
# edges
Property
Y
D: 2 names (rhombus,
parallelogram)
T - 4 sides
F1 F2 S? D?
3
Y
C: 2 names (rectangle,
parallelogram)
F - 2 pairs of
parallel sides
b)
E
D
c)
A
a)
# vertices
D & H have both
properties:
Y
A: 4 names (square,
rectangle, rhombus,
parallelogram)
B: 1 name (parallelogram)
Student descriptions
might include the following
details:
Property
AP Book G4-17
page 171
1.
4.
1.
E
N
3.
At least one
Right Angle?
Property
AP Book G4-18
page 173
Two pairs of
Parallel Sides?
Students should include the
following information
in their descriptions:
Equilateral?
3.
Quadrilateral?
Students’ answers
should include the
following information:
Shape
3.
√
7.
AP Book G4-19
page 174
1.
16
2.
A: Trapezoid
B: Trapezoid
√
C: Square
D: Square
E: Rectangle
F: Rectangle
2.
Answers will vary.
Answer Key for AP Book 4.1