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Geometry Review for GHSGT - Understanding Shapes and Angles

This review covers types of lines, angles, polygons, solid figures, Pythagorean Theorem, scientific notation, ratios, probability, and proportions for GHSGT preparation.

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Geometry Review for GHSGT - Understanding Shapes and Angles

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    1. Geometry Review for GHGST

    2. Types of lines

    3. Parallel Lines cut by a transversal Find all the angles at one point of intersection, then “pick up” the infor and “drop it” into the other point of intersection.

    6. Types of Angles Acute Angles: an angle that measures less that 90º Right Angles: an angle that measures exactly 90º (marked with a little square in the angle) Obtuse Angles: an angle that measures more than 90º but less than 180º

    7. Pairs of Angles Complementary Angles: 2 angles that add up to 90º Supplementary Angles: 2 angles that add up to 180º

    8. Hint to Angle Types!!!! Put in alphabetical order and numerical order C S 90 180

    9. Complementary Angles Two angles that add up to 90º If ?A and ?B are complementary and m?A = 63º, what is m?B? m?A+m?B=90 63 + x = 90 -63 -63 x = 27º

    10. Supplementary Angles Two angles that add up to 180º Linear Pair also add up to 180º 52 + x = 180 -52 -52 x = 128º

    11. Types of Triangles

    12. Polygons: a flat figure with 3 or more sides

    13. Solid Figures Cylinder: soup can Sphere: basketball Cone: ice cream cone Rectangular Prism: a regular box Pyramid: think Egypt (not shown) Shapes

    14. What is the difference? Perimeter: the distance around a geometric figure (cm, in, m, ft) ex. a fence around yard Area: the measure of the inside of a flat surface (cm2, in2) ex. carpet on the floor, paint on wall Volume: the measure of the inside of a 3-D figure (ft3, m3) ex. water in the pool cereal in a box

    15. Perimeter and area of polygons: You must know these!!!

    16. Volume: the one you must know Volume of a rectangular Prism V = l x w x h (length x width x height)

    17. Pythagorean Theorem Used for right triangles only!!! A² + B² = C² (or leg² + leg² = hyp²)

    18. Example of Pythagorean Theorem Find the missing leg length. a² + b² = c² 15² + x² = 25² 225 + x² = 625 -225 -225 x² = 400 sq root both sides x = 20

    19. Another example of Pythag. Thrm Find the measure of the missing side. a² + b² = c² 7² + 12² = c² 49 + 144 = c² 193 = c² sq root both sides 13.89 = c

    20. Scientific Notation Must be a single digit, decimal point, and then the rest of the number times 10 to some power (the # of digits minus one) Ex. 35,600,000 = 3.56 x 107 ( 8 digits -1) Ex. 7.9 x 103 = 7900 (exponent +1 = # of digits)

    21. Ratios Ratio: a fraction of two different quantities ratio of a to b a b ALWAYS reduce you fractions!!! Also used for probability

    22. Example of ratios In math class of 21 students, there are 14 women. What is the ratio of women to the total number of students? Women to Total Students Women Total Students 14 = 2 21 3

    23. Probability Favorable Total Possible

    24. Probability example There is a jar of jellybeans: 6 yellow, 9 red, 8 purple, 11 pink. What are the chances of pulling out a purple jelly bean if you don’t look? First add together jelly beans (total possible) 6+9+8+11= 34 jellybeans purple = 8 = 4 total 34 17

    25. Proportions: Solve by cross multiplying Solve the following: 9 = 11 18 x 9x = 18 · 11 9x = 198 divide by 9 x = 22

    26. Another Example of Proportions If 2 inch on a map equals 3 miles, how many inches would 11 miles be? Inches = Inches 2 = x miles miles 3 11 3x = 2 • 11 3x = 22 x = 7.33 inches

    27. Another example using Geometry Similar figures (same shape different size): Match sides Length = length width width 12 = 9 4 x 12x = 36 divide by 12 x = 3

    28. A final example of proportions “Slide down” 19 = x 5 3 5x = 19 • 3 5x = 57 x = 11.4

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