Angles in pattern blocks
Diagonals
Joining two nonadjacent vertices of a
polygon
For which shapes will the diagonals
always be perpendicular?
Type of
Quadrilateral
Trapezoid
Parallelogram
Rhombus
Rectangle
Square
Kite
Are diagonals
perpendicular?
For which shapes will the diagonals
always be perpendicular?
Type of
Quadrilateral
Are diagonals
perpendicular?
Trapezoid
maybe
Parallelogram
Rhombus
Rectangle
Square
Kite
For which shapes will the diagonals
always be perpendicular?
Type of
Quadrilateral
Are diagonals
perpendicular?
Trapezoid
maybe
Parallelogram
maybe
Rhombus
Rectangle
Square
Kite
For which shapes will the diagonals
always be perpendicular?
Type of
Quadrilateral
Are diagonals
perpendicular?
Trapezoid
maybe
Parallelogram
maybe
Rhombus
yes
Rectangle
Square
Kite
For which shapes will the diagonals
always be perpendicular?
Type of
Quadrilateral
Are diagonals
perpendicular?
Trapezoid
maybe
Parallelogram
maybe
Rhombus
yes
Rectangle
maybe
Square
Kite
For which shapes will the diagonals
always be perpendicular?
Type of
Quadrilateral
Are diagonals
perpendicular?
Trapezoid
maybe
Parallelogram
maybe
Rhombus
yes
Rectangle
maybe
Square
yes
Kite
For which shapes will the diagonals
always be perpendicular?
Type of
Quadrilateral
Are diagonals
perpendicular?
Trapezoid
maybe
Parallelogram
maybe
Rhombus
yes
Rectangle
maybe
Square
yes
Kite
yes
Sum of the angles of a polygon
Use a minimum of five polygon pieces to create a
5-sided, 6-sided, 7 sided, 8-sided, 9-sided, 10sided, 11-sided, or 12-sided figure. Trace on
triangle grid paper, cut out, mark and measure the
total angles in the figure.
2
1
3
4
9
http://www.arcytech.org/java/patterns/patterns_j.shtml
8
2
1
5
7
3
6
4
7
5
Sum of the angles of a polygon
Polygon
#
sides
Triangle
3
Quadrilateral
4
Pentagon
5
Hexagon
6
Heptagon
7
Octagon
8
Nonagon
9
Decagon
10
Undecagon
11
Dodecagon
12
Triskaidecagon
13
Nth
N
Total degrees
What patterns
do you see?
Sum of the angles of a polygon
Polygon
#
sides
Total degrees
Triangle
3
180
Quadrilateral
4
Pentagon
5
Hexagon
6
Heptagon
7
Octagon
8
Nonagon
9
Decagon
10
Undecagon
11
Dodecagon
12
Triskaidecagon
13
nth
n
What patterns
do you see?
Sum of the angles of a polygon
Polygon
#
sides
Total degrees
Triangle
3
180
Quadrilateral
4
360
Pentagon
5
Hexagon
6
Heptagon
7
Octagon
8
Nonagon
9
Decagon
10
Undecagon
11
Dodecagon
12
Triskaidecagon
13
nth
n
What patterns
do you see?
Sum of the angles of a polygon
Polygon
#
sides
Total degrees
Triangle
3
180
Quadrilateral
4
360
Pentagon
5
540
Hexagon
6
Heptagon
7
Octagon
8
Nonagon
9
Decagon
10
Undecagon
11
Dodecagon
12
Triskaidecagon
13
nth
n
What patterns
do you see?
Sum of the angles of a polygon
Polygon
#
sides
Total degrees
Triangle
3
180
Quadrilateral
4
360
Pentagon
5
540
Hexagon
6
720
Heptagon
7
Octagon
8
Nonagon
9
Decagon
10
Undecagon
11
Dodecagon
12
Triskaidecagon
13
nth
n
What patterns
do you see?
Sum of the angles of a polygon
Polygon
#
sides
Total degrees
Triangle
3
180
Quadrilateral
4
360
Pentagon
5
540
Hexagon
6
720
Heptagon
7
900
Octagon
8
Nonagon
9
Decagon
10
Undecagon
11
Dodecagon
12
Triskaidecagon
13
nth
n
What patterns
do you see?
Sum of the angles of a polygon
Polygon
#
sides
Total degrees
Triangle
3
180
Quadrilateral
4
360
Pentagon
5
540
Hexagon
6
720
Heptagon
7
900
Octagon
8
1080
Nonagon
9
Decagon
10
Undecagon
11
Dodecagon
12
Triskaidecagon
13
nth
n
What patterns
do you see?
Sum of the angles of a polygon
Polygon
#
sides
Total degrees
Triangle
3
180
Quadrilateral
4
360
Pentagon
5
540
Hexagon
6
720
Heptagon
7
900
Octagon
8
1080
Nonagon
9
1260
Decagon
10
Undecagon
11
Dodecagon
12
Triskaidecagon
13
nth
n
What patterns
do you see?
Sum of the angles of a polygon
Polygon
#
sides
Total degrees
Triangle
3
180
Quadrilateral
4
360
Pentagon
5
540
Hexagon
6
720
Heptagon
7
900
Octagon
8
1080
Nonagon
9
1260
Decagon
10
1440
Undecagon
11
Dodecagon
12
Triskaidecagon
13
nth
n
What patterns
do you see?
Sum of the angles of a polygon
Polygon
#
sides
Total degrees
Triangle
3
180
Quadrilateral
4
360
Pentagon
5
540
Hexagon
6
720
Heptagon
7
900
Octagon
8
1080
Nonagon
9
1260
Decagon
10
1440
Undecagon
11
1620
Dodecagon
12
Triskaidecagon
13
nth
n
What patterns
do you see?
Sum of the angles of a polygon
Polygon
#
sides
Total degrees
Triangle
3
180
Quadrilateral
4
360
Pentagon
5
540
Hexagon
6
720
Heptagon
7
900
Octagon
8
1080
Nonagon
9
1260
Decagon
10
1440
Undecagon
11
1620
Dodecagon
12
1800
Triskaidecagon
13
nth
n
What patterns
do you see?
Sum of the angles of a polygon
Polygon
#
sides
Total degrees
Triangle
3
180
Quadrilateral
4
360
Pentagon
5
540
Hexagon
6
720
Heptagon
7
900
Octagon
8
1080
Nonagon
9
1260
Decagon
10
1440
Undecagon
11
1620
Dodecagon
12
1800
Triskaidecagon
13
1980
nth
n
What patterns
do you see?
Sum of the angles of a polygon
Polygon
#
sides
Total degrees
Triangle
3
180
Quadrilateral
4
360
Pentagon
5
540
Hexagon
6
720
Heptagon
7
900
Octagon
8
1080
Nonagon
9
1260
Decagon
10
1440
Undecagon
11
1620
Dodecagon
12
1800
Triskaidecagon
13
1980
nth
n
?
What patterns
do you see?
Sum of the angles of a polygon
Polygon
#
sides
Total degrees
Triangle
3
180
Quadrilateral
4
360
Pentagon
5
540
Hexagon
6
720
Heptagon
7
900
Octagon
8
1080
Nonagon
9
1260
Decagon
10
1440
Undecagon
11
1620
Dodecagon
12
1800
Triskaidecagon
13
1980
nth
n
180(n-2)
What patterns
do you see?
Total degree of angles in polygon
Area Formulas: Triangle
http://illuminations.nctm.org/LessonDetail.aspx?ID=L577
Area Formulas: Triangle
1. Using a ruler, draw a
diagonal (from one corner
to the opposite corner) on
shapes A, B, and C.
2. Along the top edge of shape
D, mark a point that is not
a vertex. Using a ruler,
draw a line from each
bottom corner to the point
you marked. (Three
triangles should be
formed.)
3. Cut out the shapes. Then,
divide A, B, and C into two
parts by cutting along the
diagonal, and divide D into
three parts by cutting along
the lines you drew.
4. How do the areas of the
resulting shapes compare
to the area of the original
shape?
Area Formulas: Triangle
Area Formulas: Triangle
Area Formulas: Trapezoids
http://illuminations.nctm.org/LessonDetail.aspx?ID=L580
Area Formulas: Trapezoids
Do you have suggestions for finding area?
What other shapes could you use to help you?
Are there any other shapes for which you already know how to find the area?
Area Formulas: Trapezoids
18cm
15 cm
13 cm
11cm
24 cm
Connect Math Shapes Set
http://phcatalog.pearson.com/component.cfm?site_id=6&discipline_id=80
6&subarea_id=1316&program_id=23245&product_id=3502
CMP Cuisenaire® Connected Math
Shapes Set (1 set of 206)
ISBN-10: 157232368X
ISBN-13: 9781572323681
Price: $29.35
Area Formulas: Trapezoids
A = ½h(b1 + b2)
When triangles are removed from each corner and rotated, a rectangle will be formed. It’s important for
kids to see that the midline is equal to the average of the bases. This is the basis for the proof—the
midline is equal to the base of the newly formed rectangle, and the midline can be expressed as
½(b1 + b2), so the proof falls immediately into place. To be sure that students see this relationship, ask,
"How is the midline related to the two bases?" Students might suggest that the length of the midline is
"exactly between" the lengths of the two bases; more precisely, some students may indicate that it is
equal to the average of the two bases, giving the necessary expression.
Remind students that the area of a rectangle is base × height; for the rectangle formed from the
original trapezoid, the base is ½(b1 + b2) and the height is h, so the area of the rectangle (and,
consequently, of the trapezoid) is A = ½h(b1 + b2). This is the traditional formula for finding the area of
the trapezoid.
Area Formulas: Trapezoids
18cm
15 cm
13 cm
11cm
24 cm
Area Formulas: Trapezoids
Websites:
http://argyll.epsb.ca/jreed/math9/strand3/tra
pezoid_area_per.htm
dDwxNTM
Parallelograms
dDwxNTM
A
= Length x width
http://illuminations.nctm.org/LessonDetail.aspx?ID=L578
Area of Parallelogram
Can you estimate the area of Tennessee?
Area of irregular figure?
Find the area of the irregular figure.
Area of irregular figure?
Area of irregular figure?
Circles
Area = πr2
Circumference = 2 πr
or
Circumference = π d
Circles
Otis is drawing a circle with a 4 inch radius.
He wants to double the radius. How will
this affect the area of the circle?
Circles
Su is selling 12 inch diameter pumpkin pies
for $6.50. How should she adjust her
price (if she wants to be fair) when she
reduces her pies to a 10 inch diameter?
Circles
Javier’s bicycle tire has a 12 inch radius.
How far will he travel. . .
. . . in one rotation of the tire?
. . . in 10 rotations of the tire?