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Side Splitting Theorem 8.4

Side Splitting Theorem 8.4. homework. Identify parallel lines in triangles. Learn the side splitting theorem. Use the side splitting theorem to solve problems. The Side Splitting Theorem. Converse of the Side Splitting Theorem. homework. Multiple Transversal Proportionality Corollary.

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Side Splitting Theorem 8.4

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  1. Side Splitting Theorem 8.4

  2. homework • Identify parallel lines in triangles. • Learn the side splitting theorem. • Use the side splitting theorem to solve problems.

  3. The Side Splitting Theorem Converse of the Side Splitting Theorem homework

  4. Multiple Transversal Proportionality Corollary homework

  5. homework Find the Length of a Side In RST, RT||VU, SV = 3, VR = 8, and UT = 12. Find SU.

  6. B C A E D homework Find the Missing Measure using the Parallel Side In EBD, AC||ED, AE = 2, BA = 6, and AC = 9. Find ED. 6x = 72 x = 12

  7. BX BY = . XA YC homework Find the Length of a Side In ABC, XY||AC, AX = 4, XB = 10.5, and CY = 6. Find BY. 10.5(6) = 4x 63 = 4x x = 15.75

  8. homework The lines are parallel. Find x. 13x = 44

  9. homework Explain why ∆RSV ~ ∆RTU and then find RT. Prove triangles are similar. It is given that S T. R R by Reflexive Property. Therefore ∆RSV ~ ∆RTU by AA Similarity. RT(8) = 10(12) 8RT = 120 RT = 15

  10. homework Proportional Segments 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.

  11. homework ∆ABE ~ ∆ACD, find CD. x(9) = 5(3 + 9) 9x = 60

  12. homework AC || FG. ∆ABC ~ ∆FBG. Find BA to the nearest tenth of a foot. Let BF be represented by x. 24x = 6.5x + 110.5 17.5x = 110.5 x  6.3 Therefore, BA = 23.3 ft.

  13. homework 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. 24x = 15(8) 24x = 120 x = 5

  14. homework Congruent Segments Find x and y. The segments with lengths 5y and are congruent since parallel lines that cut off congruent segments on one transversal cut off congruent segments on every transversal. x = 6; y = 3

  15. homework Determine if the sides are parallel. a. b. Yes sides are proportional 5:4. Yes sides are proportional 3:5. d. c. No sides aren’t proportional. Yes sides are proportional 7:5.

  16. homework Josh wanted to measure the height of the Sears Tower in Chicago. He used a 12-foot light pole and measured its shadow at 1 P.M. The length of the shadow was 2 feet. Then he measured the length of the Sears Tower’s shadow and it was 242 feet at that time. What is the height of the Sears Tower? Since the sun’s rays form similar triangles, the following proportion can be written. The Sears Tower is 1452 feet tall.

  17. homework ABE ~ACD find BE and CD. 3x + 18 = 7.5x 4.5x = 18 x = 4

  18. homework On her trip along the East coast, Jen stops to look at the tallest lighthouse in the U.S. located at Cape Hatteras, North Carolina.At that particular time of day, Jen measures her shadow to be 1 feet 6 inches in length and the length of the shadow of the lighthouse to be 53 feet 6 inches. Jen knows that her height is 5 feet 6 inches. What is the height of the Cape Hatteras lighthouse to the nearest foot? • A • B • C • D 1.5x = 294.25 x  196 ft

  19. homework The triangles are similar. Find x, the distance across the lake. 90x = 19,800 x = 220 yards

  20. homework Find x and y. 7.2x = 72 x x = 10 yards y 8y = 46.08 y = 5.76 yards

  21. homework The triangles are similar. Find b, the brace of the ladder. 28b = 336 x = 12 inches

  22. homework Find the height of the tree. 8x = 170

  23. homework In Washington D.C. 17th, 18th, 19th and 20th streets are parallel streets that intersect Pennsylvania Ave and I St. a. How long is Pennsylvania Ave between 19th St and 18th St? 380x = 212500 b. How long is Pennsylvania Ave between 18th St and 17th St? 380x = 255000

  24. homework Find x. b. a. x2 + x = x2 – 3x + 6x – 18 24x2 – 40x = 20x2 + 40x x2 + x = x2 + 3x – 18 4x2 – 80x = 0 x = 3x – 18 4x(x – 20) = 0 –2x = –18 x = 0 or x = 20 x = 9

  25. Assignment 8.4 Side Splitting

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