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Geometry

Geometry. 7.6 Proportional Lengths. Proportional Lengths. AC and XZ are divided proportionally if…. AB. XY. =. BC. YZ. 2. 9. A. B. C. 2. 4. Example:. =. 9. 18. 18. 4. X. Y. Z. Triangle Proportionality Thm. If a line parallel to one side of a triangle intersects the

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Geometry

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  1. Geometry 7.6 Proportional Lengths

  2. Proportional Lengths • AC and XZ are divided proportionally if… AB XY . . . = BC YZ 2 9 . . . A B C 2 4 Example: = 9 18 18 4 X Y Z

  3. Triangle Proportionality Thm. • If a line parallel to one side of a triangle intersects the other two sides, then it divides those sides proportionally. big A big B = big B big A whole A small A small B whole B small A small B = side C1 small A small B whole A whole B side C2 All of these proportions, and their inverses, work. big A big B = The key is to use the easiest one to solve each problem. whole A whole B small A big A whole A big A big B side C1 = = = = small B big B whole B whole A whole B side C2 Think of it as two separate similar triangles.

  4. Corollary • If three // lines intersect two transversals,… then they divide the transversals proportionally. a c a c b d = b d

  5. Triangle Angle Bisector Thm. • If a ray bisects an angle of a triangle,… then it divides the opposite side into segments proportional to the other two sides. a c a c b = b d d

  6. D H G F E Directions: Use the given information and the triangle above to find the missing segment. 3. GE = 15 DE = 27 HF = 20 DH = ? 4. DE = 20 HF = 4 DH = 12 DG = ?

  7. A D B E C F Directions: Use the given information and the diagram to find x. 2. AB = 27 BC = 18 DE = x + 10 EF = x 3. AB = 25 – x BC = x DE = 16 EF = 4

  8. P Q R S Directions: is and angle bisector of . Find x. 2. RP = x PQ = 12.5 RS = 8 SQ = 10 3. RP = 10 PQ = 20 RS = x RQ = 15

  9. HW • P. 271 (1-7) P. 272-273 (1-14, 20, 21) Quiz 7.4-7.6 Tomorrow

  10. A few from the HW • P. 272 #5, #14

  11. An Example 16 4 12 24 18 15 20 5 15 12 = 5 4 5 15 20 = = 5 4 = 4 12 16 20 16 15 12 = 15 12 18 = = 20 16 20 16 24

  12. Solve for x. (figure not to scale) 15 Reduce by 3 27 15 20 20 = 12 12 x x 5 20 times 4 equals = 4 x times 4 equals x = 16

  13. Solve for x. Reduce by 9. 18 x = 27 x + 10 2 x 18 x 20 = 3 x + 10 27 30 x + 10 2(x + 10) = 3x 2x + 20 = 3x x = 20

  14. Solve for x. Reduce by 3. 12 15 12 x = 15 18 - x 4 x = x 5 18 - x 8 18 - x 10 18 4(18 – x) = 5x 9x = 72 x = 8 72 – 4x = 5x

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