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Objective: Students will use proportional parts of triangles and divide a segment into parts. S. Calahan 2008 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 If BD || AE, BA ≈ DE CB CD A D E Find the length of a side In ABC, BD || AE, AB = 9, BC = 21, and DE = 6. Find DC. C B A D E Find the length of a side From the Triangle Proportionality Theorem BA ≈ DE CB CD Substitute the know measures. C B A D E Find the length of a side 9 = 6 Let x = DC 21 x 9(x) =21(6) 9x = 126 x = 14 Therefore, DC = 14 B A C D E 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 A D E Midsegment of a Triangle If AE = 12 then BD = ½(12) = 6. C B A D E Divide Segments Proportionally If three or more parallel lines intersect two transversals, then they cut off the transversal proportionally. F E D AB = DE, AC = BC, and AC = DF BC EF DF EF BC EF A B C