© A Very Good Teacher 2007 Exit Level TAKS Preparation Unit Objective 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 130º50º 60º 30º

© 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 x

© 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 , 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 7 th stage contain? 6, G.05C StageNumber of Shaded Squares

© 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 x w z y 12 in 12√2 in16 in a² + b² = c² 12² + XZ² = 16² XZ² = 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 x 2x 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 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 x = = 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