NAME______________________________________DATE____________
A B C D E F
G H I J K L M
N O P Q R S
T U V W X Y
Z
Classroom Strategies Blackline Master
II - 1
57
_DATE____________NAME______________________________________DATE_______
Name__________________________________________________
Figure
58
∠1 ∠2
∠3 ∠4
∠5 ∠6
Classroom Strategies Blackline Master II - 2
∠7 ∠8
______
NAME______________________________________DATE____________
Triangle
Degrees in
angle 1
Degrees in Degrees in
Sum of
angle 2
angle 3
the angles
A
B
C
D
E
F
TYPE OF
TRIANGLE
A_____________________________________________________
B_____________________________________________________
C_____________________________________________________
D_____________________________________________________
E_____________________________________________________
F_____________________________________________________
Classroom Strategies Blackline Master
II - 3
59
NAME______________________________________DATE____________
Degrees in Degrees in Degrees in Degrees in
angle 1
angle 2
angle 3
angle 4
Sum of
the angles
A
B
C
D
E
F
TYPE OF
QUADRILATERAL
A_____________________________________________________
B_____________________________________________________
C_____________________________________________________
D_____________________________________________________
E_____________________________________________________
F_____________________________________________________
60
Classroom Strategies Blackline Master II - 4
TRIANGLE PATTERNS
Classroom Strategies Blackline Master
II - 5
61
TRIANGLE PATTERNS
62
Classroom Strategies Blackline Master II -6
TRIANGLE PATTERNS
Classroom Strategies Blackline Master
II - 7
63
QUADRILATERAL PATTERNS
64
Classroom Strategies Blackline Master II - 8
QUADRILATERAL PATTERNS
Classroom Strategies Blackline Master
II - 9
65
QUADRILATERAL PATTERNS
66
Classroom Strategies Blackline Master II - 10
II - 11
CAROLINA
NORTH
NORTH
CAROLINA
Classroom Strategies Blackline Master
67
NAME______________________________________DATE____________
Polygon
Diagonals
Angle of intersection
Do they bisect each other?
NAME______________________________________DATE____________
Polygon
68
Diagonals
Angle of intersection
Do they bisect each other?
Classroom Strategies Blackline Master II - 12
NAME______________________________________DATE____________
One-Inch Graph Paper
Classroom Strategies Blackline Master
III - 1
69
One-Centimeter Graph Paper
70
Classroom Strategies Blackline Master III - 2
NAME______________________________________DATE____________
NAME______________________________________DATE____________
Classroom Strategies Blackline Master
III - 3
71
NAME______________________________________DATE____________
72
Classroom Strategies Blackline Master III - 4
NAME______________________________________DATE____________
Classroom Strategies Blackline Master
III - 5
73
NAME______________________________________DATE____________
74
Classroom Strategies Blackline Master III - 6
OCTAGON PATTERNS
Classroom Strategies Blackline Master
III - 7
75
PENTAGON PATTERNS
76
Classroom Strategies Blackline Master III - 8
HEXAGON PATTERNS
Classroom Strategies Blackline Master
III - 9
77
NAME______________________________________DATE____________
Triangle Activities
1. Use chenille stems or pipe cleaners to make triangles with
sides corresponding to the lengths (in inches) listed below.
Figure
1
2
3
4
5
6
7
8
9
10
Side A
4
3
3
2
2
3
2
1
1
2
Side B
4
T
4
4
4
4
3
2
2
2
3
Side C
4
5
4
6
4
4
4
4
3
4
Makes a triangle?
Yes No
Yes No
Yes No
Yes No
Yes No
Yes No
Yes No
Yes No
Yes No
Yes No
2. When do you think it is possible for three lengths to make or
not make a triangle?
3. Classify the triangles you made as equilateral, isosceles,
scalene, and the angles as right, acute, or obtuse.
4. What relationships do you see between the sides and angles
of triangles? You may wish to draw more triangles to test your
ideas. Be sure to explain your thinking.
78
Classroom Strategies Blackline Master III - 10
NAME______________________________________DATE____________
Discovering Diagonals I
Draw the diagonals in each polygon. Indicate if they are
congruent (C), perpendicular (P), bisectors (B), or lines of
symmetry (S).
s
q
u
a
r
e
r
e
c
t
a
n
g
l
e
p
a
r
a
l
l
e
l
o
g
r
a
m
r
h
o
m
b
u
s
t
r
a
p
e
z
o
i
d
k
i
t
e
Classroom Strategies Blackline Master
III - 11
79
NAME______________________________________DATE____________
Discovering Diagonals II
1.
Complete the chart below.
Polygon
triangle
No. of sides/vertices
No. of diagonals
quadrilateral
pentagon
hexagon
heptagon
octagon
2. Look at the chart. What patterns do you see? Are there any
predictions you can make about other polygons and the number of
their diagonals?
3. Using your prediction or pattern what can you say about the
number of diagonals in the following polygons. Be sure to explain
your thinking.
Decagon
Dodecagon
N-gon
80
Classroom Strategies Blackline Master III - 12
.
.
.
Isometric Dot Paper
NAME______________________________________DATE____________
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Classroom Strategies Blackline Master
.
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III - 13
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81
82
Classroom Strategies Blackline Master III - 14
Classroom Strategies Blackline Master
III - 15
83
EQUILATERAL TRIANGLE GRID
84
Classroom Strategies Blackline Master III - 16
Name_______________________________________Date___/___/___
DISCOVERING DIAGONALS I
Quadrilateral
Number of
diagonals
Congruent
Diagonals
(yes/no)
Perpndicular
Diagonals
(yes/no)
Parallel
Diagonals
(yes/no)
No. of
pairs of
congruent
triangles
Square
Rectangle
Parallelogram
Rhombus
Trapezoid
Kite
Your Figure
CONCLUSIONS:
Classroom Strategies Blackline Master
III - 17
85
DISCOVERING DIAGONALS I
Draw the diagonals in each figure. Tell whether they are congruent and/or perpendicular.
RECTANGLE
SQUARE
Congruent?
Perpendicular?
Congruent?
Perpendicular?
PARALLELOGRAM
Congruent?
Perpendicular?
TRAPEZOID
Congruent?
Perpendicular?
86
RHOMBUS
Congruent?
Perpendicular?
KITE
Congruent?
Perpendicular?
Classroom Strategies Blackline Master III - 18
Name_______________________________________Date___/___/___
DISCOVERING DIAGONALS II
POLYGON
NUMBER OF
SIDES/VERTICES
NUMBER OF
DIAGONALS
triangle
quadrilateral
pentagon
hexagon
heptagon
octagon
nonagon
decagon
CONCLUSIONS:
Classroom Strategies Blackline Master
III - 19
87
Name_______________________________________Date___/___/___
QUADRILATERALS
1. Use the materials provided to make quadrilaterals with sides corresponding to the
lengths listed below. Record whether or not a quadrilateral is possible.
Color
Length of Sides (in inches)
Red
3
3
3
3
Orange
4
2
Q4
2
Yellow
4
4
2
2
Blue
2
2
2
6
Green
2
2
2
4
Pink
2
4
3
3
White
2
3
3
4
Black
1
2
3
4
Does it make a quadrilateral?
2. What type of quadrilateral did each color make?
3. Make a conjecture to explain when the four lengths will or will not make a quadrilateral.
4. Which quadrilaterals have symmetry? Line or rotational? Are certain kinds of
quadrilaterals always symmetric?
88
Classroom Strategies Blackline Master III - 20
Name_______________________________________Date___/___/___
EXPLORING POLYGONS
POLYGON
MEASUREMENT
OF SIDES
MEASUREMENT
OF DIAGONALS
Classroom Strategies Blackline Master
CONCLUSIONS
III - 21
89
Name_______________________________________Date___/___/___
PERFECTLY SQUARE
MEASUREMENT
OF DIAGONAL
90
MEASUREMENT
OF SIDE
OBSERVATIONS
Classroom Strategies Blackline Master III - 22
ATTRIBUTE GAME
Exactly one pair of
adjacent, congruent
sides.
Four right angles.
Adjacent sides are
congruent.
No sides are
congruent.
Two pairs of adjacent,
congruent sides.
Exactly one pair of
parallel sides.
Opposite sides are
congruent.
Diagonals bisect each
other.
A regular polygon.
Two pairs of parallel sides.
Congruent diagonals.
Perpendicular
diagonals.
Classroom Strategies Blackline Master
An irregular polygon.
Exactly one pair of
opposite, congruent
sides.
At least one
obtuse angle.
III - 23
91
NAME______________________________________DATE____________
Exploring Angles in Polygons
A. Cut out triangles A through E.
Tear off the corners of each
triangleand fit them side by side with the angles touching around a
point. Do each triangle separately.
1. What do you notice about the sum of the angles of these triangles?
2. Would this work for all triangles? Make some of your own and try them.
B. Cut out quadrilaterals A through E.
Tear off the corners of each quadrilateral and fit them side
by side with the angles touching around a point. Do each quadrilateral separately.
1. What did you discover?
2. What can you say about the sum of the angles of these quadrilaterals?
3. Would this work for all quadrilaterals? Make some of your own and try them.
4. How do these results compare and relate to the results you found for triangles?
92
Classroom Strategies Blackline Master III - 24
C. Try this process with pentagons and hexagons. Explore and explain what you find.
D. Make a conjecture about the relationship of the number of sides and the the sum of the interior
angles of a polygon. Explain your thinking.
Use your conjecture to find the sum of the interior angles of the following:
octagon -
decagon -
n-gon -
Classroom Strategies Blackline Master
III - 25
93
Exploring Angles - Triangles
A
B
C
E
D
94
Classroom Strategies Blackline Master III - 26
Exploring Angles - Quadrilaterals
B
A
C
D
E
Classroom Strategies Blackline Master
III - 27
95
Exploring Angles - Other Polygons
B
A
C
96
D
Classroom Strategies Blackline Master III - 28