© 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

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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

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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

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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

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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

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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

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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

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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

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• 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

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45º

45º

x

x

x√2

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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