Math 7: Geometry

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Math 7 Geometry

• ORDER INTELLIGENCE DESIGN

Pentagon Building
Nautilus Shell
Solar System
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Identifying Shapes recall the name click
Number of Sides 3
4 5 6
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Triangle
Quadrilateral
Pentagon
Hexagon
Octagon
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Angle Types

• There are four angle types you need to know.
• Name them and their definitions.

Acute
Between 0 and 90
Obtuse
Between 90 and 180
Right
90 degrees
Straight
180 degrees
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Label Each Angle Type
Acute
Right
Obtuse
Straight
What's the other name for a "right" angle?
Lindquist Angle!
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A Few Questions .

• 1) An angle that measures 54 degrees is
  _________.
• a) Acute b) Obtuse c) Straight d) Right

• A 180 degree angle is a __________ angle.
• a) Acute b) Obtuse c) Straight d) Right

3) Perpendicular lines make what kind of angles?
Right Angles!!!!!
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Triangle Types Choose ALL possible choices from
the words belowScalene Equilateral Acute
Right Isosceles Obtuse

• This triangle has all sides equal.
• 2) This triangle has no sides equal and all
  angles less than 90 degrees.
• 3) This triangle has two equal sides.
• 4) This triangle has an angle greater than 90 and
  less than 180 degrees.
• 5) The angles of this triangle are 90, 45 and 45.

Equilateral
Scalene. Acute.
Isosceles
Obtuse
Right. Isosceles.
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How many degrees in the 3 lts of a
triangle?_______
180
How many degrees in the missing angle below?
58
70
52
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Find the value of n
This is isosceles, so it has two congruent angles
as well as two congruent sides. What does the
base angle on the left equal?
48
n like the one on the right ?
Therefore .. 2n 48 180. Solve this!
n
2n 48 180 - 48 -48 2n
132 n 66 ? !
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Angle Triangle Questions
1) An acute triangle has three acute angles.
Does an obtuse triangle have 3 obtuse angles?
Why or why not?
No! The three angles of a triangle sum to 180.
All obtuse angles are greater than 90, so three
of them would sum to 270 or more.
2) True or false and why An obtuse triangle
can never be isosceles?
False! One example is a triangle with angles of
100, 40 and 40. Also, see the diagram below.
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The Quadrilateral Family

• Papa Parallelogram

Opposite Sides Parallel Equal Opposite Angles
Equal Angles Sum to 360
Randy Rectangle
Rebecca Rhombus
Parallelogram 4 Equal Sides
Parallelogram 4 Rt lts Congruent Diagonals
Squiggy Square
Everything !!!!!
What is important about each?
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The Tricky Trapezoid
What makes a trapezoid tricky?
110
110
It is kind of like a parallelogram but it only
has one pair of parallel sides! A parallelogram
has two pairs.
70
70
How is a trapezoid like a parallelogram?
The interior angles add up to 360. Check out the
angles..
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Find the Missing Angle in Each Figure
105
75
105
93
75
x
115
Remember the interior angles of a quadrilateral
add up to 360.
62
x
90
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Quadrilateral QuestionsAlways. Sometimes.
Never.
A rectangle is a parallelogram.
Always the opposite sides of a rectangle are
congruent.
A rhombus is a square.
Sometimes. But a rhombus does not have to have a
right angle.
A trapezoid is a paralellogram.
Never! A trapezoid only has one pair of parallel
sides.
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Match the Name to the Pic

• 1) Rectangle only
• 2) Parallelogram
• 3) Square
• 4) Rhombus

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Key Terms Key Pictures
1) Define Complementary.
Two lts add up to 90
2) Define Supplementary
Two lts add up to 180
What is the trick for remembering that
complementary means 90 and supplementary means
180?
C comes before S, 90 before 180
3) What is the complement of 40?
50
4) What is the supplement of 100?
80
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Find the complement and supplement of an angle of
40 degrees.
Complement 50 Supplement 140.
What is the difference between the supplement and
complement of 40?
90
Will the difference between the complement and
supplement of any given angle always be 90? Why
or why not?
Yes! Think about it Complementary adds up to
90 and supplementary to 180. The difference
between those two numbers is 90 ? .
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Complementary or Supplementary?
Which picture is which and find the value of n.
Supplementary 2n 68 180 n 56
2n
68
Complementary 9 3n 63 90
63
3n
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Perimeter and Area
Perimeter measures the _____________ of a
figure. Area measures the _____________ of a
figure.
outside
10 in
32 in
inside
adds
multiplies
Which operation?
Perimeter ______. Area __________.
Find the perimeter and area of the rectangle
above.
Perimeter Area
Add all sides. 84 inches 10 in32 in10 in 32in
Area length x width 10 in x 32 in 320 sq. in.
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Circles Circumference Area
Circumference is like perimeter but only
applies to a circle. Area doesnt change it is
all about how much is inside.
What is the trick to remember the formulas?
Cherry Pie is delicious. Apple pies are,
too. C pd A pr2
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Parts of a Circle
For our purposes, there are two main parts of a
circle we need to know .. diameter and
radius. What is the difference?
The diameter goes all the way across. The radius
only goes halfway.
diameter
radius
If the diameter if a circle is 18 inches, what is
the radius?
The radius only goes halfway across so it must be
half of 18 inches 9 inches.
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Find the Circumference and Area of the circle.
C p d (d is diameter)
10 m
C 3.1416 x 20 m C 62.832 m
A p r2 (r is radius)
A 3.1416 x 10 m x 10 m A 314.16 m2
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Surface Area of a Rectangular Prism
How many faces does this prism have?
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Ill name one side. You name its opposite partner.
FRONT
LEFT
TOP
BACK
RIGHT
BOTTOM
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Finding The Surface Area
Step 1 Find the fronts area.
TOP
5 in x 8 in 40 in2 x 2 80 in2
FRONT
5 in
Why double the 40?
The Back!
2) Find the top area and double it.
8 inches
4 in
8 in x 4 in 32 in2 x 2 64 in2
RIGHT
3) Find the area of the right and double it
because of the left partner or equal face.
4 in x 5 in 20 in2 x 2 40 in2
Add the areas of the faces to get the surface
area)
80 in2 64 in2 40 in2 184 in2
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Surface Area of a Cylinder
What shapes do you get when you unfold a cylinder?
Two congruent circles on the top and bottom and a
rectangle.
If the width of the rectangle on the side is the
height, how do you find the length?
Radius 10 Height 25
It is the circumference of the circles.
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Computing the Surface Area
The reference sheet gives the following formula
for the surface area of a cylinder SA 2prh
2pr2
Substitute and crank out the antza ? . SA
2(3.1416)(10)(25) 2(3.1416)(102)
1570.8 628.32 2199.12
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WINK What I Need To Know
Polygon Types
Complemetary Supplementary Vertical Angles
Geometry
Perimeter Area Circumference
Angle Types
Surface Area