Similar Triangles II

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Similar Triangles word problems and applications in the real world.

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Similar Triangles II

  1. 1. Image Source: http://www.canon.com
  2. 2. Image Source: http://www.olympusamerica.com
  3. 3. Image Source: http://www.canon.com
  4. 4. Image Source: Dirt River Radio Band Photos taken by Passy Why does a low light Zoom Camera Lens cost a lot of money? Because it has a lot of very precisely shaped movable geometrically shaped optics inside it, which all have to be mathematically perfect in their shape and movement. Lots of precise work to make, means lots of $ on the price tag.
  5. 5. Image Source: http://www.rags-int-inc.com Similar Triangle “Bow Tie” mathematics is involved with Optics Eg. Camera Lenses and Eyes Glasses.
  6. 6. S.F. = 24 / 8 = 3 Therefore L = 3 x 5 L = 15 Because A = D we know that AB is parallel to DE (Alternates) The two angles each side of “C” are Equal (Vertical Angles) B = E by Alternates, or because total triangle = 180 THEREFORE TRIANGLES ARE SIMILAR BY AAA RULE. A C B D E 5 24 8 L = ?
  7. 7. 24 L 8 5 We can also use proportion of matching sides: A C B D E 5 24 8 L = ? = Set up the sides and then Cross Multiply 24 x 5 = L x 8 120 = 8L Solve this equation by dividing by 8 15 = L or L = 15
  8. 8. A C ED B 4 8 10 L = ? Calculate the length “L” of DE Scale Factor = 8 / 4 = 2 Because of Similarity, AC corresponds to CE AB corresponds to DE Because they are matching sides. DE = 2 x 10 L = 20 ABC ~ CDE by AAA Vertical Angles at Point C
  9. 9. Similar Triangles are used to determine the Height of tall objects using shadow lengths. Diagrams for these questions have Triangles inside Triangles h = ? 2m 12m 84m
  10. 10. ABC and ADE share common A They also each have a Right Angle ABC ~ ADE (by AAA) Next step is to find the Scale Factor, and then use it to get “h” h = ? 2m 12m 84m A B C E D
  11. 11. S.F. = AE / AC S.F. = 84 / 12 S.F. = 7 2m 12m C E h = ? 84m A B D The large triangle is Seven Times bigger than the small one So the Height of the Tree is 7 times the height of the person. h = 7 x 2 = 14m
  12. 12. 2m 12m C E h = ? 84m A B D h 84 2 12= h x 12 = 84 x 2 12h = 168 h = 14m Set up the sides and then Cross Multiply Solve by dividing by 12 We can also work out this question by setting up the Ratios and then Cross Multiplying.
  13. 13. Redraw this diagram and use Similar Triangles on the shadow Lengths to work out the Height of the mobile phone tower . Draw the standard Triangles inside Triangles Diagram h = ? 1.8 m 6m 60m
  14. 14. ABC ~ ADE (by AAA) S.F. = 60/6 = 10 h = 10 x 1.8 h = 18m We have found the Scale Factor, and then used it to get “h” h = ? 1.8m 6 m 60m A B C E D
  15. 15. http://passyworldofmathematics.com/ All slides are exclusive Copyright of Passy’s World of Mathematics Visit our site for Free Mathematics PowerPoints

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