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Exploring Parallel Lines and Proportional Parts in Triangles

In this lesson, students will learn how to use proportional parts of triangles to divide segments into parts. Key concepts include the definition of a midsegment and the Triangle Proportionality Theorem. Through examples involving triangles and proportional segments, learners will practice finding unknown lengths when provided with certain parameters. The lesson emphasizes the relationship between parallel lines and proportional segments, providing the foundation for more advanced geometry concepts. Homework is assigned to reinforce the understanding of these principles.

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Exploring Parallel Lines and Proportional Parts in Triangles

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  1. Lesson 6-4 Parallel Lines and Proportional Parts

  2. Objectives • Use proportional parts of triangle • Divide a segment into parts

  3. Vocabulary • Midsegment: a segment whose endpoints are the midpoints of two sides of the triangle

  4. S Answer: Example 1 In ∆RST, RT // VU, SV = 3, VR = 8, and UT = 12. Find SU. From the Triangle Proportionality Theorem, Multiply. Divide each side by 8. Simplify.

  5. B Example 2 In ∆ABC, AC // XY, AX=4, XB=10.5 and CY=6. Find BY. Answer: 15.75

  6. Since the sides have proportional length. Answer: since the segments have proportional lengths, Example 3 In ∆DEF, DH=18, HE=36, and 2DG = GF. Determine whether GH // FE. Explain. In order to show that we must show that

  7. X Answer: No; the segments are not in proportion since Example 4 In ∆WXZ, XY=15, YZ=25, WA=18 and AZ=32. Determine whether WX // AY. Explain.

  8. Summary & Homework • Summary: • A segment that intersects two sides of a triangle and is parallel to the third side divides the two intersected sides in proportion • If two lines divide two segments in proportion, then the lines are parallel • Homework: Page 312 (14-26)

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