© A Very Good Teacher 2007 Exit Level TAKS Preparation Unit Objective 6.
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Transcript of © A Very Good Teacher 2007 Exit Level TAKS Preparation Unit Objective 6.
© A Very Good Teacher 2007
Exit Level
TAKS Preparation UnitObjective 6
© A Very Good Teacher 2007
Solve by drawing• A few important geometric concepts
• Complementary Angles add up to 90º
• Supplementary Angles add up to 180º
• The sum of the interior angles of a triangle is 180º
6, G.04A
100º
40º 40º
130º50º
60º30º
© A Very Good Teacher 2007
Solve by drawing, cont…• When the problem describes a geometric
figure, draw it!
• Example: If and are supplementary angles and is x, what equation can be used to find y, ?
6, G.04A
m Bm A
BA
A Bx180 - x
© A Very Good Teacher 2007
Geometric Patterns• Make a table.• Use y=, 2nd Graph to see which answer gives
you the same table!• Example: The measure of an interior angle is
shown for each of the three regular polygons shown below. Which expression best represents the measure of one interior angle of a polygon with n sides?
60º 90º 108º
Number of Sides
Measure of 1 angle
3 60
4 90
5 108
6, G.05A
© A Very Good Teacher 2007
Parallel Lines• When a set of parallel lines
is crossed by a transversal the following are true– Corresponding Angles are
congruent– Alternate Interior and
Exterior Angles are congruent
– Same side Interior and Exterior Angles are Supplementary
– Consecutive Angles are Supplementary
6, G.05B
© A Very Good Teacher 2007
Fractals and more patterns• Given a sequence of geometric figures, you will
be asked to predict the number of figures, shaded figures, etc in a future stage.
• Create a table and extend it• Example: How many shaded squares will the 7th
stage contain?
6, G.05C
Stage Number of Shaded Squares
1 1
2 5
3 9
4
5
6
7
131721
25
© A Very Good Teacher 2007
Right Triangles• Three important formulas (on your formula
chart)
• Pythagorean Theorem (to find missing sides when 2 sides are known)
a² + b² = c²
• 30º- 60º - 90º
x, x√3, 2x
• 45º - 45º - 90º
x, x, x√2
6, G.05D
© A Very Good Teacher 2007
Using the Pythagorean Theorem• In order to use the Pythagorean Theorem,
you must know at least 2 sides of the right triangle!
• Example: In the figure below, what is the length of XZ?
6, G.05D
xw
z
y
12 in
12√2 in 16 ina² + b² = c²12² + XZ² = 16²144 + XZ² = 256
-144 -144 XZ² = 112
√XZ² = √112 XZ = 10.58
© A Very Good Teacher 2007
Using 30º-60º-90º Formulas• The triangle must have angle measure of
30º, 60º, and 90º!
• Example:
• What if the short
leg is 4 inches?
• What if the longest
side is 12?
30º
60º
x2x
x√3
4=
4√3
2(4) = 82x = 12, so x = 6
6√3
6=
6, G.05D
© A Very Good Teacher 2007
• The triangle must have angle measures of 45º, 45º, and 90º!
• Notice that a right isosceles triangle is a 45º-45º-90º
Using 45º-45º-90º Formulas
6, G.05D
45º
45º
x
x
x√2
© A Very Good Teacher 2007
Using 45º-45º-90º Formulas, cont…
• Example: ∆XYZ is shown below. If XY = 8 inches, what is the area of ∆XYZ?
X
YZ
x
x
x√2= 8
x√2 = 8√2 √2
x = 5.66 5.66 =
5.66 =Area of ∆ = ½bh
Area of ∆XYZ = ½(5.66)(5.66)
Area of ∆XYZ = 16
© A Very Good Teacher 2007
Transformations• Three types of Transformations
• Translation (slide)
• Rotation (turn)
• Reflection (flip over)
6, G.10A