Transcript 7.2 - Quadrilaterals & Other Polygons - nss-gr9

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Focus Time
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of class?
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during class
YES
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you don’t get tempted
(for JUST 75 mins!)
YES
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taken away and given to a VP
NO
Homework
Pg. 381 #2, 3, 6, 7b, 10(a,e)
Pg. 391 #1c, 2b, 3c, 6, 7a
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Remember!
Triangles
Quadrilaterals
>>
>>
All interior angles add to
180°
All interior angles add to
360°
All exterior angles add to
360°
All exterior angles add to
360°
Find m
Find a
a
m
94°
120°
56°
130°
75°
100°
Find t
Find h
Challenge!
h
79°
83°
t
119°
39°
33°
84°
Find m
m
120°
75°
130°
The interior angles of a quadrilateral
always add up to 360°
m + 120 + 75 + 130 = 360
m + 325 = 360
m + 325 – 325 = 360 – 325
m = 35°
Find a
a
94°
56°
100°
The exterior angles of a quadrilateral
always add up to 360°
a + 94 + 56 + 100 = 360
a + 250 = 360
a + 250 – 250 = 360 – 250
a = 110°
Find t
79°
t
The interior angles of a
quadrilateral always add up to 360°
t + 79 + x + 119 = 360
83° x
119°
Can’t find t without x
t + 79 + 97 + 119 = 360
x + 83 = 180
x + 83 – 83 = 180 - 83
x = 97°
t + 295 = 360
t + 295 - 295 = 360 - 295
t = 65°
Find h
Start with what you need to find and
work backwards!
h
o
84°
39°
33°
h + o = 180
Can’t find h without o
Find h
Start with what you need to find and
work backwards!
h
o
84°
39°
33°
h + o = 180
Can’t find h without o
m
The interior angles of a
quadrilateral always add up to 360°
o + 39 + 84 + m = 360
Can’t find o without m
Find h
Start with what you need to find and
work backwards!
h
o
84°
39°
33°
h + o = 180
Can’t find h without o
m e
m + e = 180
Can’t find m without e
The interior angles of a
quadrilateral always add up to 360°
o + 39 + 84 + m = 360
Can’t find o without m
Find h
Start with what you need to find and
work backwards!
h
o
84°
h + o = 180
Can’t find h without o
h + 114 = 180
h = 66°
39°
33°
m e
m + e = 180
Can’t find m without e
m + 57 = 180
m = 123
The interior angles of a
quadrilateral always add up to 360°
The interior angles of a triangle
always add up to 180°
e + 33 + 90 = 180
e = 57°
o + 39 + 84 + m = 360
Can’t find o without m
o + 39 + 84 + 123 = 360
o = 114°
Parallelogram Sketchpad Demo
Parallelogram Rule
>>
a
b
>>
b
a
Opposite angles are always equal in a parallelogram!
C - rule
>
>
a
b
When there are two parallel lines and a 3rd line that intersects
both of them, the inside of the C-shape add up to 180°
a + b = 180°
55°
a
125°
b
b
Challenge!
>>
a
b
>>
>>
a
c
d
>>
70°
c
55°
a
125°
b
In a parallelogram, opposite angles are equal
55°
125°
125°
55°
In a parallelogram, opposite angles are equal
a = 125°
b = 55°
>>
a
b
>>
70°
c
>>
a
70°
>>
70°
c
Since the two horizontal lines are
parallel, we can use the ‘C’ rule
a + 70 = 180
a + 70 – 70 = 180 - 70
a = 110°
>>
110°
70°
>>
70°
c
Since the two horizontal lines are
parallel, we can use the ‘C’ rule
a + 70 = 180
a + 70 – 70 = 180 - 70
a = 110°
>>
110°
70°
>>
110°
70°
Since the two horizontal lines are
parallel, we can use the ‘C’ rule
a + 70 = 180
a + 70 – 70 = 180 - 70
a = 110°
>>
a
b
>>
c
d
e
The interior angles of a
triangle add up to 180
e + e + 90 = 180
2e + 90 = 180
2e + 90 – 90 = 180 - 90
2e = 90
2
2
e = 45°
e
Start with any info you have (the
triangle)
Since the triangle has 2 sides of
equal length, the 2 corners have
the same angle (lets call them ‘e’)
>>
a
d
45°
b
>>
c
45°
Start with any info you have (the
triangle)
Since the triangle has 2 sides of
equal length, the 2 corners have
the same angle (lets call them ‘e’)
The interior angles of a
triangle add up to 180
e + e + 90 = 180
2e + 90 = 180
2e + 90 – 90 = 180 - 90
2e = 90
2
2
e = 45°
c + 45 = 180
c + 45 – 45 = 180 - 45
c = 135°
>>
a
d
45°
b
>>
135° 45°
Start with any info you have (the
triangle)
Since the triangle has 2 sides of
equal length, the 2 corners have
the same angle (lets call them ‘e’)
The interior angles of a
triangle add up to 180
e + e + 90 = 180
2e + 90 = 180
2e + 90 – 90 = 180 - 90
2e = 90
2
2
e = 45°
c + 45 = 180
c + 45 – 45 = 180 - 45
c = 135°
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Checking out polygons on Sketchpad
Sum of Interior Angles = 180(n-2)
n represents how many sides the polygon has
Pentagon
n=5
Hexagon
n=6
Heptagon
n=7
SIA = 180(5-2)
SIA= 180(3)
SIA= 540°
SIA = 180(6-2)
SIA= 180(4)
SIA= 720°
SIA = 180(7-2)
SIA= 180(5)
SIA= 900°
Use the new equation to
find the sum of the interior
angles of a triangle
What angle does each
corner of a regular octagon
have?
Find w
How many sides does a
polygon have if the sum of
its interior angles is 1800°?
Challenge!
w
Use the new equation to find the sum of the interior angles
of a triangle
Sum of interior angles = 180(n-2)
A triangle has 3 sides so n = 3
Sum of interior angles = 180(3-2)
Sum of interior angles = 180(1)
Sum of interior angles = 180°
We already knew this
What angle does each corner of a regular
octagon have?
Sum of interior angles = 180(n-2)
An octagon has 8 sides so n = 8
Sum of interior angles = 180(8-2)
Sum of interior angles = 180(6)
Sum of interior angles = 1080°
Since a regular octagon means that all 8 corners have the same
angle, we divide 1080° by 8 (the # of corners) to get 135° for
each corner.
How many sides does a polygon have if the sum of
its interior angles is 1800°?
Sum of interior angles = 180(n-2)
We don’t know the number of sides (n) but we know the sum of
interior angles
1800 = 180(n-2)
180
180
10 = n-2
10 + 2 = n – 2 + 2
12 = n
A polygon with an interior angle sum of 1800° has 12 sides.
Find w
Since the triangle has 2 sides of equal
length, it also has 2 corners of equal angle
x
w
w
w + w + x = 180
2w + x = 180
Can’t find w without x
Find w
Since the triangle has 2 sides of equal
length, it also has 2 corners of equal angle
x
w
w + w + x = 180
w
2w + x = 180
Can’t find w without x
2w + 108 = 180
w = 36°
Since this is a regular pentagon (n = 5)
Sum of interior angles = 180(5-2)
Sum of interior angles = 180(3)
Sum of interior angles = 540°
Since all 5 corners are equal, you get x by dividing 540° by 5.
This means x = 108°