M.2 Angle Polygons (2).notebook
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Types of Polygons
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M.2 Angle Polygons (2).notebook
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Measuring Angles
70
80
90
60
100
90
120
80
70
130
130
60
140
30
150
20
110
120
40
100
110
50
7°
50
140
40
150
160
30
10
170
20
0
160
180
10
170
0
180
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M.2 Angle Polygons (2).notebook
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Drawing Angles
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M.2 Angle Polygons (2).notebook
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Formulas and Substitution
A formula is a short hand kinda like a text message letters represent a value which is given in the question Formulas usually have to be manipulated to find out the unknown. 4
M.2 Angle Polygons (2).notebook
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Area of Composite Shapes
arectangle, parallelogram = bxh
atriangle = bxh
2
acircle = pi r2
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M.2 Angle Polygons (2).notebook
April 08, 2014
M.2 Angle Properties of Polygons
Outcome:
M.3 ‐ Solve problems that involve:
• triangles
• quadrilaterals
• regular polygons.
What will we do?
­determine the sum and measure of angles in a polygon
­explore types of angles in polygons
­explore tessellations of polygons
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M.2 Angle Polygons (2).notebook
April 08, 2014
Vocabulary
Regular Polygon a closed figure with 3 or more straight sides and equal side and angle measurements
Examples:
squares, equilateral triangles, regular octagons Interior Angle An angle inside a polygon
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M.2 Angle Polygons (2).notebook
April 08, 2014
1. Draw an equilateral triangle.
a) What is the measure of each side length?
b) What is the measure of each interior angle?
c) What is the sum of the interior angles?
2. Draw a square triangle.
a) What is the measure of each side length?
b) What is the measure of each interior angle?
c) What is the sum of the interior angles?
d) If you connect the diagonals, how many triangles are created?
3. Draw a regular pentagon.
a) What is the measure of each side length?
b) What is the measure of each interior angle?
c) What is the sum of the interior angles?
d) If you connect the diagonals, how many triangles are created?
4. Draw a regular hexagon.
a) What is the measure of each side length?
b) What is the measure of each interior angle?
c) What is the sum of the interior angles?
d) If you connect the diagonals, how many triangles are created?
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M.2 Angle Polygons (2).notebook
Figure
# of sides (side length)
April 08, 2014
# triangles
Measure of Interior Angles
Sum of Interior Angles
Equilateral Triangle
Square
Regular Pentagon
Equilateral Hexagon
Do you notice any patterns?
­What is the relationship between the number of sides and the number of triangles?
­What is the relationship between the number of sides and the sum of the interior angles?
­What is the relationship between the number of sides and the measure of each interior angle?
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M.2 Angle Polygons (2).notebook
April 08, 2014
Can we make predictions about...
1. The sum of interior angles of:
a) a regular octagon (8 sides)? 1080
b) a regular decagon (10 sides)? 1440
c) a regular dodecagon (12 sides)? 1800
2. The measure of each interior angle of:
a) a regular octagon (8 sides)?135
b) a regular decagon (10 sides)? 144
c) a regular dodecagon (12 sides)?150
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M.2 Angle Polygons (2).notebook
April 08, 2014
Example
Tracy is building a wooden display frame. She needs to decide what shape to make the frame. She thinking about what kinds of cuts and how many cuts she would have to make. She considers the following shapes:
Regular Hexagon
Square
Isoceles Triangle
Determine what kinds of interior angles Tracy will need to create for each shape.
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M.2 Angle Polygons (2).notebook
April 08, 2014
Regular Hexagon
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M.2 Angle Polygons (2).notebook
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Square
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M.2 Angle Polygons (2).notebook
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Isoceles Triangle
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M.2 Angle Polygons (2).notebook
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You Try!
Tracy also considers using the following shapes for her frame:
Regular Pentagon
Isoceles Trapezoid
Parallelogram
a) Describe the interior angles she might create for each shape.
b) Which angles are equal to each other?
c) Classify each angle as right, obtuse or acute.
d) How many of each type of angle does each shape have?
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M.2 Angle Polygons (2).notebook
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What can we say about irregular polygons?
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M.2 Angle Polygons (2).notebook
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Practice!
p. 230 #s 1 ­ 6
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M.2 Angle Polygons (2).notebook
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Tessellations
Tessellate
to cover an area using the repetition of geometric shapes, with no overlaps and no gaps
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M.2 Angle Polygons (2).notebook
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How can we tell if something tessellates??
Cut out the shapes to find out!
Your Task:
1. Cut out the shapes. 2. See if you can fit them together like a puzzle, with no overlaps and no gaps.
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M.2 Angle Polygons (2).notebook
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M.2 Angle Polygons (2).notebook
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this will leave a gap...
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M.2 Angle Polygons (2).notebook
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Is there another way to tell if a polygon will tessellate?
Your Task:
For each of the shapes you cut out...
1. What is the sum of the interior angles where they meet?
2. What do you notice about the shapes that tessellate, and the shapes that do not?
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M.2 Angle Polygons (2).notebook
April 08, 2014
Your Task:
1. Create your own tessellation!
2. Measure and label your angles!
3. Colour it!
D
B
A
C
C
D
C
D
B
A
C
B
A
A
B
D
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