fourth six weeks’ test review. for the purposes of this presentation
TRANSCRIPT
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Fourth Six Weeks’ Test Review
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For the purposes of this presentation...
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Assume that triangles which appear to be right triangles are.
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Assume that lines that appear to be perpendicular are.
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4
25x =10
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The The Pythagorean Pythagorean TheoremTheorem
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6
8
x =10
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12
18
x 21.63
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20
16
x=12
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1515
24
x
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1515
24
X= 9
1212
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Special Right Special Right TrianglesTriangles
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45o
x
12 2
=12
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x
10
1010 2
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30o
20x
y
10
10 3
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10 10
10
x5 3
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Find the Geometric mean between 4 and 25.
=10
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NM=9, MK=4, Find JM.
=6
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What equation can be formed?
g
t
m
2 2 2g t m
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What kind of triangle has sides 41, 40 and 9?
Right
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What kind of triangle has sides of 8, 12 and 18? Obtuse
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Find the leg of the right triangle:
15
17
x =8
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Find x
8
8
x 8 2
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An equilateral triangle has a side of 12. What is its altitude?
6 3
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Which ratio is: The opposite leg over the hypotenuse?
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The Sine Ratio
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Which ratio is: The adjacent leg over the hypotenuse?
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The Cosine Ratio
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What makes up the tangent ratio?
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The opposite leg over the adjacent leg
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Set Up the Trig Set Up the Trig ratio to find xratio to find x
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20
28o
x
cos 2820
x
17.66
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9x
50o
9sin 50
x
11.75
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x21
32
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x21
32
Tan x = 21/32
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x21
32
1 21tan
32x
33.27
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What’s true about an interior and exterior angle of a polygon?
Supplementary
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For polygons to “fit” around a vertex, the sum of their interior angles must be 360
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A regular n-gon has lines of symmetry and rotational of360/n degrees
n
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Find the sum of the interior angles of a decagon:
1440
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Find the measure of 1 interior angle of a regular 18-gon
160
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Find the sum of the exterior angles of a 55-gon
360
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Find the measure of one exterior angle of a regular 24-gon
15
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The sum of the interior angles of what polygon is 4500? 27-gon
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The measure of 1 interior angle of what regular polygon is 170?
36-gon
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The measure of 1 exterior angle of what regular polygon is 8?
45-gon
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A regular octagon has 8 lines of symmetry and what degree of rotation? 45
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The sum of its interior angles is 4 times the sum of its exterior angles. decagon
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?
What regular polygon is missing
Another hexagon
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What regular polygon is missing
?
Another Octagon
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What’s the symmetry of a regular decagon?
10 lines, 36 degr. rotational
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Find x (Given a regular octagon)
x
X = 90 degrees
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What 3 regular polygons will tessellate the plane?
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Equilateral triangles
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Regular Hexagons
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Squares
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Which special quadrilateral has the symmetry described...
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- No lines
- 180o rotational
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Answer: Parallelogram
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Complete the Complete the Theorem….Theorem….
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The diagonals of a parallelogram_________.
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…bisect each other.
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Opposite sides of a parallelogram are__________.
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…congruent.(They are also parallel, but that is in the definition, not a theorem.)
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If the opposite angles of a quadrilateral are congruent, then__________
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…then the quadrilateral is a parallelogram.
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Consecutive angles of a parallelogram are ____________.
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Supplementary.
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Always, Always, Sometimes, or Sometimes, or Never...Never...
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The diagonals of a parallelogram ____ bisect each other.
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Always
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A quadrilateral is _____ a parallelogram,
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Sometimes
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The End