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7.1 Ratio and Proportions

7.1 Ratio and Proportions. Ratio and Proportion. _______________________________________ ________________________________________ _______________________________________ Word form: Colon form: Fraction form: _______________________________________.

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7.1 Ratio and Proportions

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  1. 7.1 Ratio and Proportions

  2. Ratio and Proportion • _______________________________________ • ________________________________________ • _______________________________________ • Word form: • Colon form: • Fraction form: • _______________________________________

  3. A poster is 3 feet long and 20 inches wide. Find the ratio of length to width. • Comparing feet: • Comparing inches:

  4. 60 A 10 60 E 30 5x B • Find the ratio of AE to BE. • Find the ratio of the largest angle of Triangle A to smallest angle of triangle B.

  5. 3. A telephone pole 7 meters tall snaps into two parts. The ratio of the two parts is 3:2. Find the length of each part.

  6. A B 6 C D 10

  7. The measures of the angles of a triangle are in the ratio of 3:4:5. Find the measures of each angle.

  8. 7.2 Properties of Proportions

  9. A proportion is a set of two equal ratios: _____________________________________ _____________________________________

  10. The Means and Extremes Property: • _____________________________________ • ______________________________________ • ______________________________________

  11. Properties of Proportions:

  12. A D B C E • If CE=2, AB=6 and AD=3 then EB=______ • 2. If AB=10, DB=8 and CB=7.5 then EB=______

  13. A D B C E • BA=12, BE=10, EC=5 • Find BD=______ DA=_____

  14. 7.3 Similar Polygons

  15. __________________________________________ • __________________________________________ • __________________________________________ • Two polygons are similar if their vertices can be paired so that: • _________________________________________ • _________________________________________ • __________________________________________ • __________________________________________

  16. B W A C V X Y Z E D List congruent Angles: List Proportions of sides:

  17. If polygons are similar then the ratio of the lengths of two corresponding sides is called the Scale Factor 12 y D D` C C` 30 22 x z A` 50 B` A B 30 a) Scale Factor: a) Find x, y, z:

  18. The ratio of the perimeters of two similar figures is equal to the Scale Factor. 12 z D D` C C` x 2.5 10 5 A` 3 B` A B y a) Scale Factor: a) Find x, y, z:

  19. a) Scale Factor: b) Angle D`=____ 21 D D` C C` 60 100 6 5 A` 12 B` A B 4 c) Find CB, A`D`, DC:

  20. 7.4 Proving Triangles areSimilar

  21. Postulate 15: ________________________ ___________________________________ ___________________________________ A X Y B C

  22. When there are triangles within Trianlges: • _______________________________ • _______________________________

  23. Are the triangles similar? Find the scale factor._______ Solve for x=_______ 3 5 1 x

  24. Find x=______ and y=______: Scale Factor=____ x 8 3 y 3 4

  25. A D O B C

  26. 7.5 More Similar Triangles

  27. Theorem 7.1: __________________________ ______________________________________ ______________________________________ ______________________________________ 12 3 5 20

  28. Theorem 7.2: ___________________________ _______________________________________ 12 28 3 7 5 20

  29. How do we know what sides of the triangles to compare? • _______________________________________ • ________________________________________ • __________________________________

  30. What reason are the Triangles ~? 6 10 3 5 3 5 6 6 6 10

  31. Def of ~ ______________________________ ______________________________________ ______________________________________ Means and Extremes Property: __________ _____________________________________ _____________________________________

  32. A D B C E

  33. 10 x y 9 15 16 Solve for x and y: Scale Factor?____

  34. 7.6 Proportional Lengths

  35. Divide Proportionally means: ________________________________________ ________________________________________ Triangle Proportionality Theorem: ____________________________________________________________________________________________________________ a c b d

  36. Corollary: ____________________________ _____________________________________ a c b d

  37. Triangle Angle Bisector: _______________________________________ _______________________________________ _______________________________________ _______________________________________ c a b d

  38. Examples: 20 5x 10 5

  39. x 10 12 24

  40. x 4 2 x+2

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