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Parallel Lines and Proportional Parts

Parallel Lines and Proportional Parts. Chapter 7-4. Use proportional parts of triangles. Divide a segment into parts. midsegment.

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Parallel Lines and Proportional Parts

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  1. Parallel Lines and Proportional Parts Chapter 7-4

  2. Use proportional parts of triangles. • Divide a segment into parts. • midsegment Standard 12.0 Students find and use measures of sidesand of interior and exterior angles of triangles and polygons toclassify figures and solve problems. (Key) Lesson 4 MI/Vocab

  3. C D A B E 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. • The converse is true also.

  4. 24 C 9 D A 26 B 9.75 E Example #1

  5. Find the Length of a Side Lesson 4 Ex1

  6. Find the Length of a Side Substitute the known measures. Cross products Multiply. Divide each side by 8. Simplify. Lesson 4 Ex1

  7. A. 2.29 B. 4.125 C. 12 D. 15.75 Lesson 4 CYP1

  8. In order to show that we must show that Determine Parallel Lines Lesson 4 Ex2

  9. Since the sides have proportional length. Determine Parallel Lines Lesson 4 Ex2

  10. A • B • C A. yes B. no C. cannot be determined Lesson 4 CYP2

  11. C DE // AB and DE = AB D E A B Midsegment Theorem • The midsegment connecting the midpoints of two sides of the triangle is parallel to the third side and is half as long.

  12. Midsegment of a Triangle Lesson 4 Ex3

  13. Use the Midpoint Formula to find the midpoints of Midsegment of a Triangle Answer:D (0, 3), E (1, –1) Lesson 4 Ex3

  14. Midsegment of a Triangle Lesson 4 Ex3

  15. If the slopes of slope of slope of Midsegment of a Triangle Lesson 4 Ex3

  16. Midsegment of a Triangle Lesson 4 Ex3

  17. Midsegment of a Triangle First, use the Distance Formula to find BC and DE. Lesson 4 Ex3

  18. Midsegment of a Triangle Lesson 4 Ex3

  19. A.W (0, 1), Z (1, –3) B.W (0, 2), Z (2, –3) C.W (0, 3), Z (2, –3) D.W (0, 2), Z (1, –3) Lesson 4 CYP3

  20. A • B A. yes B. no Lesson 4 CYP3

  21. A • B A. yes B. no Lesson 4 CYP3

  22. A C E B D F Parallel Proportionality Theorem • If 3 // lines intersect two transversals, then they divide the transversals proportionally.

  23. U T S SP // TQ // UR Corresponding Angle Thm. 11 15 P 9 Q R Find ST Example #2 Parallel Proportionality Theorem

  24. J 9 37.5 K L 7.5 x 13.5 M N y Solve for x and y Example #4 Solving for x What is JL? 37.5 – x

  25. J 9 37.5 K L 7.5 x 13.5 M N y Solve for x and y Example #4 Solving for y JKL~JMN AA~Theorem

  26. Proportional Segments MAPS In the figure, Larch, Maple, and Nuthatch Streets are all parallel. The figure shows the distances in city blocks that the streets are apart. Find x. Lesson 4 Ex4

  27. Proportional Segments Notice that the streets form a triangle that is cut by parallel lines. So you can use the Triangle Proportionality Theorem. Triangle Proportionality Theorem Cross products Multiply. Divide each side by 13. Answer: 32 Lesson 4 Ex4

  28. In the figure, Davis, Broad, and Main Streets are all parallel. The figure shows the distances in city blocks that the streets are apart. Find x. A. 4 B. 5 C. 6 D. 7 Lesson 4 CYP4

  29. Congruent Segments Find x and y. To find x: Given Subtract 2x from each side. Add 4 to each side. Lesson 4 Ex5

  30. The segments with lengths are congruent since parallel lines that cut off congruent segments on one transversal cut off congruent segments on every transversal. Congruent Segments To find y: Lesson 4 Ex5

  31. Congruent Segments Equal lengths Multiply each side by 3 to eliminate the denominator. Subtract 8y from each side. Divide each side by 7. Answer:x = 6; y = 3 Lesson 4 Ex5

  32. A. B.1 C.11 D.7 Find a. Lesson 4 CYP5

  33. Find b. A. 0.5 B. 1.5 C. –6 D. 1 Lesson 4 CYP5

  34. Homework Chapter 7-4 • Pg 410 13-21, 26 – 27, 32 – 36, 61

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