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January 11, 2012

January 11, 2012. 1) Write your homework in your agenda: Proportional Parts worksheet 2) Take out your parallel lines worksheet and leave it on your desk. 3) Take out your Cornell Notes from yesterday. 4) Take out your angle quiz. Answers to Proving Parallel Lines.

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January 11, 2012

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  1. January 11, 2012 1) Write your homework in your agenda: Proportional Parts worksheet 2) Take out your parallel lines worksheet and leave it on your desk. 3) Take out your Cornell Notes from yesterday. 4) Take out your angle quiz.

  2. Answers to Proving Parallel Lines 1) 130o 9) 50o 2) 128o 10) 63o 3) 66o 11) x = 6 4) 100o 12) x = 7 5) 90o 13) x = -7 6) 81o 14) x = 6 7) 53o 15) x = 12 8) 58o 16) x = 8

  3. CD BC D FG EF C B AD FG A AG AB AB AE E F G What is Two Transversal Proportionality Theorem? • If three or more parallel lines intersect two transversals, then they cut off the transversals proportionally. BC AC = = AF EF CD = = AE

  4. In the diagram 1  2  3, and PQ = 9, QR = 15, and ST = 11. What is the length of TU? Two Transversal Proportionality Theorem

  5. SOLUTION: Because corresponding angles are congruent, the lines are parallel and you can use Two Transversal Proportionality Theorem PQQR ST Parallel lines divide transversals proportionally. = TU 9 11 = Substitute 15 TU 9 ● TU = 15 ● 11 Cross Product 165 = Divide each side by 9 and simplify. 9TU 55 3 • So, the length of TU is 55/3 or 18 1/3.

  6. Two-Transversal Proportionality Example Solve for x and y 26x = 15(30) x = 15y = 16.5(26) y = 28.6

  7. Triangle Proportionality Theorem If a line parallel to one side of a triangle intersects the other two sides, then it divides the two side proportionally. If TU ║ QS, then

  8. Converse of the Triangle Proportionality Theorem If a line intersects two sides of a triangle and separates the sides into corresponding segments of proportional lengths, then the line is parallel to the third side. If , then TU ║ QS.

  9. Example 1 In the diagram AB ║ ED, BD = 8, DC = 4, and AE = 12. What is the length of EC?

  10. Example 2 Given the diagram, determine whether MN ║GH MN is not parallel to GH.

  11. In the diagram KL ║ MN. Find the values of the variables. Try This…

  12. To find the value of x, you can set up a proportion. Solution Write the proportion Cross product Distributive property Add 13.5x to each side. Divide each side by 22.5 13.5(37.5 – x) = 9x 506.25 – 13.5x = 9x 506.25 = 22.5 x 22.5 = x

  13. To find the value of y, you can set up a proportion. Solution Write the proportion Cross product property Divide each side by 9. 9y = 7.5(22.5) y = 18.75

  14. R 9 Q • Try this one too! 3 P S y T 20

  15. January 13, 2012 1) Grab a Computation Challenge, keep it face down and put your name on the back 2) Write your homework in your agenda: Study Guide 3) Take out your worksheet and leave it on your desk.

  16. Building Construction: You are insulating your attic, as shown. The vertical 2 x 4 studs are evenly spaced. Explain why the diagonal cuts at the tops of the strips of insulation should have the same length. Use proportionality Theorems in Real Life

  17. Because the studs AD, BE and CF are each vertical, you know they are parallel to each other. Using Theorem 8.6, you can conclude that Use proportionality Theorems in Real Life DE AB = EF BC • Because the studs are evenly spaced, you know that DE = EF. So you can conclude that AB = BC, which means that the diagonal cuts at the tops of the strips have the same lengths.

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