Download Notes package

EM40S
UNIT
MAEM40S
Polygons
Lesson 1
L1 Regular Polygons
Polygon - ______________________________________________________________
Regular Polygon – ______________________________________________________
______________________________________________________________________
All triangles are Polygons!
Name
Description
Example
Acute
Obtuse
Right
Special Triangles
Equilateral
Two sides congruent
No sides congruent
Polygon Song
Have students identify work-related
situations where regular polygons may
be used (decorative patio)
Activity Pg. 222
Polygon
# of Sides
3
4
5
6
7
8
9
10
11
12
MAEM40S
Polygons
Lesson 1
Diagonal – _____________________________________________________________
______________________________________________________________________
To find the number of diagonals in a polygon with n sides, use the following formula:
n(n − 3)
2
Example: Find the number of diagonals of an octagon.
€
Example: Find the number of diagonals in the following polygon:
Assignment: Have students create logo using symmetry and polygons
Diagonal Practice:
1.
Find the number of diagonals in a:
a. pentagon
b. nonogon
c. decagon
2. Find the number of diagonals in the following polygon:
a.
3. If a regular polygon has 44 diagonals, what polygon is it?
MAEM40S
Polygons
L2 Interior Angles
Interior Angle: ____________________________
_________________________________________
_________________________________________
Sum of Interior Angles:
Size of each Interior Angle:
Ex: What is the third interior angle of the triangle?
Ex: What is the fourth interior angle of the quadrilateral?
Ex: The diagram shows a pentagon. What is the size of the angle x°?
Ex: Find the sum of interior angles in a regular hexagon.
Ex: Calculate the size of each interior angle in a regular octagon.
Lesson 2
MAEM40S
Polygons
Lesson 2
Central Angle
The central angle is the angle made at the _______________ of the polygon by any
two adjacent vertices of the polygon.
All central angles would add up to 360° (a full circle), so the measure of the central
angle is 360 divided by the number of sides. Or, as a formula:
where n is the number of sides.
Example: Find the measure of a central angle of a regular quadrilateral.
Example: Find the measure of a central angle of a regular polygon with the 10 sides.
Example: If a regular polygon has central angles of 45 degrees, how many sides does
it have?
Assignment: Pg. 230; #1-6, 7 d,e, 8 b,c,d, 9
MAEM40S
Polygons
Lesson 3
L3 Exterior Angles
Exterior Angle: _________________________________________________________
______________________________________________________________________
Note: when you add up the Interior Angle and Exterior Angle, you get a straight line,
and a straight line is 180˚.
Note: _________________________________________________
______________________________________________________
Size of exterior angles =
Number of sides on polygon =
Ex: A regular polygon has equal exterior angles of 72˚.
a) Calculate the size of each interior angle in the regular polygon.
b) Calculate the number of sides in the regular polygon.
Ex: What is the sum of the exterior angles of an octagon?
Ex: What is the size of one exterior angle of a regular decagon (ten-sided polygon)?
Assignment: Exterior Angle Worksheet
MAEM40S
Polygons
Lesson 3
L3 Exterior Angles Worksheet
1.
Find the size of each exterior angle in a polygon that has 12 sides.
2. Find the number of sides of a regular polygon whose exterior angles contains 5
degrees.
3. Find the size of each exterior angle in a polygon that has 9 sides.
4. Find the number of sides of a regular polygon whose exterior angles contains
10 degrees.
5. Find the number of sides of a regular polygon each of whose exterior angles
contains 15 degrees.
6. What is the size of one exterior angle of a regular decagon (ten-sided
polygon)?
7. One exterior angle of a regular polygon is 20°. How many sides does it have?
8. What is the size of one exterior angle of a regular heptagon (seven-sided
polygon)?
MAEM40S
Polygons
Lesson 4
L4 Quadrilaterals
Quadrilateral: __________________________________________________________
______________________________________________________________________
Diagonal: ______________________________________________________________
______________________________________________________________________
Quadrilaterals
Not Quadrilaterals
Concave Quadrilateral
Irregular Quadrilateral
Types of Quadrilaterals:
Shape
Properties
Picture
MAEM40S
Polygons
Lesson 4
MAEM40S
Polygons
Lesson 4
Sometimes polygons have more than one name. What are three names for a square?
Ex: What is the name of this quadrilateral?
Ex: What is the name of this quadrilateral?
Ex: Which of the following statements is false?
a) A rectangle is also a parallelogram
b) A trapezoid (trapezium) is also a parallelogram
c) A rhombus is also a parallelogram
d) A rhombus is also a kite
Ex: The shape shown in the diagram is:
MAEM40S
Polygons
Lesson 4
Ex: ABCD is a parallelogram What is the size of angle A?
Ex: ABCD is a kite What is the size of angle B?
Ex: ABCD is an isosceles trapezoid (isosceles trapezium). What is the size of angle A?
Assignment: Pg. 241; #1-7
MAEM40S
Polygons
Lesson 4
L4 Quadrilaterals Worksheet
1.
Circle the polygons
2. Name the quadrilaterals in Question 1
3. Name the regular polygons in Question 1
4. Sketch a polygon that has each property below. Classify each polygon.
a) Each interior angle is 60˚.
b) There are five equal sides.
5. Kylie designs and sews quilts. Describe a property of polygons that she might
use in a quilt. Include a diagram with your description.
MAEM40S
Polygons
Lesson 4
6. Which convex quadrilaterals have each property?
a) Two pairs of equal sides
b) Four right angles
c) Equal diagonals
d) Equal angles at opposite vertices
7. The diagonals in a square are perpendicular. The diagonals cross at their
midpoints. Record the names of other types of quadrilaterals to complete the
chart
Property
A quadrilateral with this
property
A quadrilateral without
this property
Diagonals are
perpendicular
Diagonals cross at
their midpoints
8. Hayley is the lighting director for a theatre in Manitoba. She wants to place a
spotlight so that it shines on the centre of a rectangular stage. How can Hayley
use a property of rectangles to find the centre of the stage? Use the rectangle
below in your explanation.
9. Ty says that if you know all the angle measures in a triangle, you will know
whether the sides are equal. Do you agree? Explain with diagrams.