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Parallel Lines and Proportional Parts 6-4

Parallel Lines and Proportional Parts 6-4. Objective: Students will use proportional parts of triangles and divide a segment into parts. S. Calahan 2008. Triangle Proportionality Theorem.

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Parallel Lines and Proportional Parts 6-4

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  1. Parallel Lines and Proportional Parts 6-4 Objective: Students will use proportional parts of triangles and divide a segment into parts. S. Calahan 2008

  2. Triangle Proportionality Theorem • If a line is parallel to one side of a triangle and intersects the other two sides in two distinct points, then it separates these sides into segments of proportional lengths. C B D If BD || AE, BA ≈ DE CB CD E A

  3. Find the length of a side • In ABC, BD || AE, AB = 9, BC = 21, and DE = 6. Find DC. C B D E A

  4. Find the length of a side • From the Triangle Proportionality Theorem BA ≈ DE CB CD • Substitute the know measures. C B D E A

  5. Find the length of a side 9 = 6 Let x = DC 21 x 9(x) =21(6) 9x = 126 x = 14 Therefore, DC = 14 C B D E A

  6. Triangle Midsegment Theorem A midsegment of a triangle is parallel to one side of the triangle, and its length is ½ the length of that side. If B and D are midpoints of AC and EC respectively, BD || AE and BD = ½ AE. C B D E A

  7. Midsegment of a Triangle • If AE = 12 then BD = ½(12) = 6. C B D E A

  8. Divide Segments Proportionally • If three or more parallel lines intersect two transversals, then they cut off the transversal proportionally. F E D A AB = DE, AC = BC, and AC = DF BC EF DF EF BC EF B C

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