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Slide 3: 5 : 7 is an example of a RATIO—the quotient of x divided by y, where y is NOT equal to zero. A RATIO can be written as: x to y x : y x/y ? All of these ratios are read “x to y” (sometimes x is to y). Slide 4: To simplify a ratio, divide out the common factors. Example: Simplify 24 : 36 9 : 24 3a : 15 2 : 3 (common factor: 12) 3 : 8 (common factor : 3) a : 5 (common factor: 3) Slide 5: B A D C 16 8 70 Use PARALLELOGRAM ABCD to express the ratio in simplest form. AB to BC BC : AD m?A : m?D 8 : 16 or 1 : 2 16 : 16 or 1 :1 70 : 110 or 7 : 11 Slide 6: RATIO is also used to find out the distribution of values of a whole into parts. EXAMPLE: The measures of two complementary angles are in the ratio 2 : 3. Find their measures. SOLUTION: Since 2 to 3 Is the ratio, let 2x and 3x represent the actual angle measures. Thus, 2x + 3x = 90 5x = 90 x = 18 1st angle= 2x 2nd angle= 3x = 2(18) = 36 = 2(18) = 54 Slide 7: The Ratio of two supplementary angles is 3 to 7. SOLUTION: Let 3x = 1st angle 7x = 2nd angle 3x + 7x = 180 10x = 180 x = 18 = 3(18) = 54 = 7(18) = 126 Slide 8: The Ratio of two complementary angles is 1 to 5. SOLUTION: Let x = 1st angle 5x = 2nd angle x + 5x = 90 6x = 90 x = 15 = 1(15) = 15 = 5(15) = 75 Slide 9: Do this: The measures of the acute angles of a right triangle are in the ratio 15:3. Find their actual measures. SOLUTION: Let 15x = 1st acute angle 3x = 2nd acute angle 15x + 3x = 90 18x = 90 X = 5 = 15(5) = 75 = 3(5) = 15 Slide 10: The measures of the acute angles of a right triangle are in the ratio 6:3. Find their actual measures. SOLUTION: Let 6x = 1st acute angle 3x = 2nd acute angle 6x + 3x = 90 9x = 90 X = 10 = 6(10) = 60 = 3(10) = 30 Slide 11: Another: Find the measures of the angles of a triangle that are in the ratio 2 : 5 : 8. SOLUTION: Let 2x = 1st angle 5x = 2nd angle 8x = 3rd angle 2x + 5x + 8x = 180 15x = 180 x = 12 = 2(12) = 24 = 5(12) = 60 = 8(12) = 96 Slide 12: Another: The measures of the angles of a triangle are in the ratio 1 : 2 : 3. SOLUTION: Let x = 1st angle 2x = 2nd angle 3x = 3rd angle 1x + 2x + 3x = 180 6x = 180 x = 30 = 1(30) = 30 = 2(30) = 60 = 3(30) = 90 Slide 13: Find the measures of the angles of a triangle that are in the ratio 2: 7 : 9. SOLUTION: Let 2x = 1st angle 7x = 2nd angle 9x = 3rd angle 2x + 7x + 9x = 180 18x = 180 x = 10 = 2(10) = 20 = 7(10) = 70 = 9(10) = 90 Slide 14: PROPORTION means the equality of 2 ratios. In symbols, it is a/b = c/d or 1st term 2nd term 3rd term 4th term Note: b and d must not be zero a:b = c:d Slide 15: The product of the means equals the product of the extremes. OR Example: find x, x : 5 = 15 : 25 a:b = c:d 25x = 5(15) 25x = 75 x = 3 ad = bc Slide 16: Identify the MEANS and the EXTREMES and look for the missing term (x). 1. 3 : x = 9 : 21 2. (x+2) : 8 = (3x – 7) : 16 9x = 63 x = 7 8(3x-7) = 16(x+2) 24x-56 = 16x+32 24x-16x = 32+56 8x = 88 x = 11 2(90-x) = 8x 180 – 2x = 8x -2x-8x = -180 -10x = -180 x = 18 Slide 17: A Ratio ? is the quotient of x divided by y, where y is not equal to zero. ? can be written as x to y, x : y, or x/y. ? is simplified by dividing out the common factors. What is a ratio? Slide 18: A Proportion = is the equality of 2 ratios. = can be written as a : b = c : d or a/b = c/d, where a and d are the extremes and b and c are the means, with b and d not equal to zero. = has extremes product equal to the means product What is a proportion? Slide 19: A. Express in RATIO, and simplify whenever possible: BC : AB ED : BC AE : AD AC : AD AB : AD QUIZ Slide 20: B. In this figure, if KJ/KF = GI/GF, find IJ if the perimeter of the triangle FIJ is 40. Slide 21: Thank you and Good bye… You do not have the permission to view this presentation. In order to view it, please contact the author of the presentation.