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Sec 8.5 #38 p . 495

Sec 8.5 #38 p . 495. Roller Coaster Loop Problem. E. 40. 30. F. I separated the 2 triangles. E. 40. 30. F. I separated the 2 triangles. AD & BC are perpendicular to ground, DC. Then AD, BC, & EF are all perpendicular to DC, so they are all parallel to each other. E. 40. 30.

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Sec 8.5 #38 p . 495

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  1. Sec 8.5 #38 p. 495 Roller Coaster Loop Problem

  2. E 40 30 F I separated the 2 triangles

  3. E 40 30 F I separated the 2 triangles AD & BC are perpendicular to ground, DC. Then AD, BC, & EF are all perpendicular to DC, so they are all parallel to each other.

  4. E 40 30 F ~ ~ < A = <FEC & < CBD = <FED by Corresponding parts Postulate Draw arcs using Inspire tools.

  5. E 40 30 F ADC ~ EFC & BCD ~ EFD by AA Similarity

  6. E 40 30 F EF FCEFDF 40 DC 30 DC = = & by def’n of Similar triangles, sides are proportional

  7. E 40 30 F Use the addition property of equality: EF EFFCDF 40 30 DC DC + = +

  8. E 40 30 F Combine fractions: + EF EFFC DF 40 30 DC + =

  9. E 40 30 F Simplify: EF EFDC 40 30 DC + =

  10. E 40 30 F Simplify: EF EF 40 30 + = 1

  11. E 40 30 F Find common denominator & combine fractions: 3(EF) 4 (EF) 120 + = 1

  12. E 40 30 F Simplify: 7 (EF) 120 = 1

  13. E 40 30 F Multiply both sides by 120: 7 (EF) = 120

  14. E 40 30 F Divide both sides by 7: 7 (EF) =120 7 7

  15. E 40 30 F Simplify: EF =120 7 or length of EF = 17 1/7

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