1. © A Very Good Teacher 2007 Exit Level TAKS Preparation Unit Objective 6

2. © 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 130º50º 60º 30º

3. © 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 AB x 180 - x

4. © A Very Good Teacher 2007 Geometric Patterns Make a table. Use y=, 2 nd 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 360 490 5108 6, G.05A

5. © 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

6. © 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 7 th stage contain? 6, G.05C StageNumber of Shaded Squares 11 25 39 4 5 6 7 13 17 21 25

7. © 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

8. © 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 x w z y 12 in 12√2 in16 in a² + b² = c² 12² + XZ² = 16² 144 + XZ² = 256 -144 -144 XZ² = 112 √XZ² = √112 XZ = 10.58

9. © 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 x 2x x√3 4= 4√3 2(4) = 82x = 12, so x = 6 6√3 6= 6, G.05D

10. © 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 x x x√2

11. © 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 x = 5.66 5.66 = Area of ∆ = ½bh Area of ∆XYZ = ½(5.66)(5.66) Area of ∆XYZ = 16

12. © A Very Good Teacher 2007 Transformations Three types of Transformations Translation (slide) Rotation (turn) Reflection (flip over) 6, G.10A