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Chapter 6.6 Notes: Use Proportionality Theorems

Chapter 6.6 Notes: Use Proportionality Theorems. Goal: You will use proportions with a triangle or parallel lines. Theorem 6.4 Triangle Proportionality Theorem : If a line parallel to one side of a triangle intersects the other two sides, then it divides the two sides proportionally.

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Chapter 6.6 Notes: Use Proportionality Theorems

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  1. Chapter 6.6 Notes: Use Proportionality Theorems Goal: You will use proportions with a triangle or parallel lines.

  2. Theorem 6.4 Triangle Proportionality Theorem: If a line parallel to one side of a triangle intersects the other two sides, then it divides the two sides proportionally. • Theorem 6.5 Converse of the Triangle Proportionality Theorem: If a line divides two sides of a triangle proportionally, then it is parallel to the third side.

  3. Ex.1: In the diagram, RS = 4, ST = 6, and QU = 9. What is the length of RQ?

  4. Ex.2: On the shoe rack shown, AB = 33 cm, BC = 27 cm, CD = 44 cm, and DE = 25 cm. Explain why the gray shelf is not parallel to the floor.

  5. Ex.3: Find the length of YZ. Ex.4: Determine whether

  6. Theorem 6.6: If three parallel lines intersect two transversals, then they divide the transversals proportionally. • Theorem 6.7: If a ray bisects an angle of a triangle, then it divides the opposite side into segments whose lengths are proportional to the lengths of the other two sides.

  7. Ex.5: In the diagram, are all congruent and GF = 120 yards, DE = 150 yards, and CD = 300 yards. Find the distance HF between Main Street and South Main Street.

  8. Ex.6: In the diagram, Use the given side lengths to find the length of RS.

  9. Ex.7: Find the length of AB. a. b.

  10. Ex.8: In the diagram, MS = 15, SN = 20, and RP = 12. What is the length of MP? Ex.9: In the diagram, Use the given side lengths to find the length of DC.

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