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Math Help - parallel lines and transversals

  1. #1
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    parallel lines and transversals

    Lines l1 and l2 intersect each other and 3 parallel lines, l3, l4, and l5, at the points shown below. The ratio of the perimeter of triangle ABC to the perimeter of triangle AFG is 1:3. The ratio of DE to FG is 2:3. What is the ratio of AC to CE?

    I know that answer is 1:1 but I'm not sure how to prove it..
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    Last edited by sarahh; April 2nd 2011 at 03:10 AM.
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    "I'm not sure how to prove it.." You're not sure or you don't know?

    Indication: Use The Fundamental Theorem of Similarity and/ or Thales' Theorem.
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    So I looked both of those up and it's still unclear how to use them for this proof.. so how do you prove it?
    Last edited by sarahh; April 2nd 2011 at 10:08 AM.
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    "So I looked both of those up and it's still unclear how to use them for this proof" ... in ten minutes, well, yeah, obviously it's unclear.

    What exactly don't you understand?
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    I don't understand how to show the result that those lengths are 1:1, so how do you do it??
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    "Indication: Use The Fundamental Theorem of Similarity and/ or Thales' Theorem." Remember that?

    "The ratio of the perimeter of triangle ABC to the perimeter of triangle AFG is 1:3. The ratio of DE to FG is 2:3." This is what you know, use it and The Fundamental Theorem of Similarity for two conveniently chosen triangles. After that thinghs should be clear.
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    Yeah I know about similarity, what I don't know is how to relate it to this problem? Anyone else wanna help take a crack at this?
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    Sooo... you're waiting for someone to solve your problem and refuse to think, nice, very nice -_-

    "how to relate it to this problem" You sure know that theorems?

    "Lines l1 and l2 intersect each other and 3 parallel lines, l3, l4, and l5, at the points shown below."
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    Simply restating the problem isn't helping and just because I don't see what to do, doesn't mean I'm not thinking about it. So is there anyone who does?
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  10. #10
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    parallel lines and transversals

    Hi Sarahh.
    Draw a triangle ABC with a base BC Mark the midpoints of AB and AC m and n. Draw a line mn. Measure the perimeters of the two triangles . Compare all ratios of the sides of both triangles. Then repeat the procedure with your diagram but with the given perimeters or other info


    bjh
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