Final Exam Review

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Final Exam Review Geometry
2
Geometry Review

• The Math 7 Final Exam will test, among other
  things, how well you can do algebra, geometry,
  proportions percents, number sense patterns
  and graphing.

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Geometry

• The geometry questions you see on your final will
  fall (for the most part) under four
  classifications.

Missing Parts
Vocabulary
Geometry
3D Figures
Shapes
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Geometry

• You will do a question or two on each slide. If
  you get it right, just go on to the next slide.
  If you get it wrong, click the arrow at the
  bottom of the page to complete a tutorial on that
  kind of equation. Be absolutely positive that
  you write your work on scrap paper and you will
  have to hand it in for credit. Click the arrow
  to begin.

Click to Begin
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The Three Angles of a Triangle
180

• The three angles of a triangle add up to _____.
  Find n in each diagram

57
90
n
90 57 147 180 147 33
6
How many degrees in the 3 lts of a
triangle?_______
180
How many degrees in the missing angle below?
58 52 110 180 110 70
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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Find the value of n
The vertex angle of an isosceles triangle
measures 80. Find the measure of each of the
base angles.
80
The three angles sum to 180, so N N 80 180
n
n
2N 80 180 - 80 -80 2N
100 N 50
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Tricky Triangle Questions
Johnny says an equilateral triangle is not
isosceles. Is Johnny right or wrong?
Johnny is wrong. An isosceles triangle has two
sides equal. Two of the sides of the equilateral
triangle ARE equal. It does not matter that the
third sides is, too.
Is it possible for a triangle to have two right
angles?
No. Numerical explanation two of the angles
would already sum to 180 (90 90). There would
be no room for a third angle. Geometric
explanation Two sides of the triangle would
never meet.
90
90
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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.
click here to return
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 Pythagorean Theorem

• The Pythagorean Theorem says a2 b2 c2. You
  can use this formula as long as you always
  remember that c is the hypotenuse. Another way
  to do the Pythagorean theorem is leg2 leg2
  hyp2.
• Find n in each diagram

n2 62 102 n2 36 100 - 36 - 36 n2
64 N 8
10
12
n
6
n
5
52 122 n2 25 144 n2 13 n
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Word Problem

• A ladder is leaning against the side of a
  building. The ladder is 15 ft long and the base
  of the ladder is at a point that is 9 feet from
  the house. How high up the house is the ladder?

n2 92 152 n2 81 225 n2 144 n
12
15
n
9
Time to go back to the D Test.....
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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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Pairs of Angles
Find the value of n in each diagram.
36
7n 8
100
n
These angles are called ________ and they are
_______.
These angles are called ___________ and they sum
to ______.
supplementary
vertical
equal
180
7n 8 36 - 8 - 8 7n 28
7 7 n 4
100 n 180 -100 - 100 n 80
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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 27 n 63 90
63
n
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Key Points to Remember
180

• The three angles of a triangle add up to ______.
• Vertical angles are always ___.
• Complementary means two angles that add up to
  ____ and supplementary means adds up to ____.

90
180
Return to the Diagnostic Test
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3D Geometry Formulas

• When you get a three dimensional geometry
  question, you will be given a formula to follow.
  Relate the parts of the figure to the letters in
  the formula. If the radius of the figure is 10
  in and the height is 5 inches, find the volume.

V pr2h V (3.14)(10 in)(10 in)(5 in) V 1570
in3
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3D Geometry Formulas

• When you get a three dimensional geometry
  question, you will be given a formula to follow.
  Relate the parts of the figure to the letters in
  the formula.
• SA 2lw 2wh 2lh

SA 2(10)(3)2(3)(4)2(10)(4) SA 60 24
80 SA 164 in2
4 in
3 in
10 in
click here to return
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The 3 Angles of a Triangle

• The three angles of a triangle are 70, 60 and n.
  Find n.

50
If you missed it, click here
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Pythagorean Theorem

• A skateboard ramp measures 5 ft high and 12 ft
  along the ground. How long is the ramp that the
  skater rides on?

13 ft
If you got this wrong, click here
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Vocabulary

• Here are some questions based on definitions..
• 1) what is the supplement of a 70 degree angle?
• 2) Find n in the diagram of vertical angles
  below

110
7
5n - 8
27
One or more wrong, click here
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3D Geometry

• Find the surface area of the rectangular prism
  below. Use the formula SA 2lw 2wh 2lh.

5 in
4 in
256 in2
12 in
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3D Geometry

• Find the volume of the cylinder below. The
  radius is 10 inches and the height is 5 inches.
  Use p 3.14

1570 in3
if yu missed this or the previous one, click here
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Thats All Folks !!!!!