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7.4: Parallel Lines and Proportional Parts

7.4: Parallel Lines and Proportional Parts. p. 362-369. Th. 7-5 : Proving Parallel lines with overlapping triangles. If a line intersects 2 sides of a triangle and separates the sides into corresponding segments of proportional lengths, then the line is parallel to the 3 rd side. . D. 2.

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7.4: Parallel Lines and Proportional Parts

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  1. 7.4: Parallel Lines and Proportional Parts p. 362-369

  2. Th. 7-5: Proving Parallel lines with overlapping triangles • If a line intersects 2 sides of a triangle and separates the sides into corresponding segments of proportional lengths, then the line is parallel to the 3rd side. D 2 They are proportional, so AB must be parallel to DC B 5 7.5 3 A C

  3. Th. 7.6: Segment though the middle of a triangle • A segment whose endpoints are the midpoints of two sides of a triangle is parallel to the 3rd side, and its lengths is ½ the length of the 3rd side. QG = ½ AB So if QG = 20 in , AB = IF AB = 12 ft, QC = If AB = 2x+4, and QG = 3x-5, find x

  4. Ex Triangle ABC has vertices A(0,2), B (12,0) and C (2,10). • Find the coordinates of D (midpoint of BC) • Find the coordinates of E (midpoint of AB) • Mathematically determine if DE is parallel to AC • Mathematically show that DE = ½ AC

  5. Corollary 7-1 • If 3 or more parallel lines intersect two transversals, then they cut off the transversals proportionally. Solve for x

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