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Homework Help: Help on triangle proof question

  1. Dec 17, 2005 #1
    Hello,
    Here is the question:
    question2.jpg
    Here are 2 different ways i tried to approach the question:
    In the first way, i tried using pythagoreom theorem by making a right angle, but after i did the question i realized since it did not say it was a right triangle, ic annot assume there is a 90 degrees angle and i cannot use the pythagoras theorem.
    part1question2.jpg
    Second way i tried using vector addition. However you can see at the end i was stuck.
    part2question2.jpg
    though i believe vector addition is the way to solve this problem, however we had never done any problems involving the squared of a vector unless it was using the pythagoras theorem,
    any suggestions in what i did wrong or what i could do?

    Sorry for my messy writing hehe.

    thanks
    byron
     
  2. jcsd
  3. Dec 17, 2005 #2

    Tide

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    Byron,

    Try this. Drop a perpendicular from A to the line segment BC. Call its length h and the distance between the intersection point and the midpoint x. Now you can use Pythagoras to solve for x and h from which you can calculate AD.
     
  4. Dec 17, 2005 #3

    Hurkyl

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    I know why you can't do it with vector addition: nowhere in your work did you make use of the fact that D is the midpoint of the line segment BC.

    (In fact, you didn't even made use of the fact that D is on the line through B and C!)
     
  5. Dec 17, 2005 #4
    didnt i do it in the first try? but if you drop a perpendicular from A to line segment BC then how would u prove that it is a right angle? but i think i did that in first try..

    though i am going to try coordinate proofs right now :D i think that is the solution
     
  6. Dec 17, 2005 #5

    Hurkyl

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    I only looked at your vector addition approach. I agree that ought to be the easiest solution. (unless you're particularly adept with synthetic geometry)
     
  7. Dec 17, 2005 #6
    i got the answer by using coordinate proofs and making LS = RS

    thanks for all your help :D
     
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