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Geometry 7.4 Parallel Lines and Proportional Parts

C. B. D. E. A. Geometry 7.4 Parallel Lines and Proportional Parts. Triangle Proportionality Theorem (Theorem 7.4) If a line is || 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.

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Geometry 7.4 Parallel Lines and Proportional Parts

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  1. C B D E A Geometry7.4 Parallel Lines and Proportional Parts • Triangle Proportionality Theorem (Theorem 7.4) • If a line is || 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.

  2. In the figure, AE || BD. Find the value of x. E 8 D x + 5 C x B 6 A Example

  3. C B D E A Theorem 7.5 • If a line intersects two sides of a triangle and separates the sides into corresponding segments of proportional lengths, then the line is || to the third side. then BD || AE

  4. A 6 8 D E 4 3 B C Example • Determine whether DE || BC. • Yes because 6/3 = 8/4

  5. A E D B C Theorem 7.6: Triangle Midsegment Theorem • Midsegment: A segment with endpoints that are midpoints of two sides of the triangle. • A midsegment of a triangle is || to one side of the triangle and its length is one-half the length of the third side.

  6. Example • Refer to the figure and Example #3 on page 407 • The example uses the midpoint formula, the slope formula and the distance formula to verify coordinates of midpoint, parallelism, and lengths of segments.

  7. X A D B E C F Corollary 7.1 • If 3 or more || lines intersect 2 transversals, then they cut off the transversals proportionally.

  8. 15 9 12 x a b c Example • In the figure, a || b || c. Find the value of x. • 20

  9. Corollary 7.2 • If 3 or more || lines cut off  segments on one transversal, then they cut off  segments on every transversal.

  10. Homework #48 • p. 411 13-18, 21-29 odd, 32-38 even, 54-55

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