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Proof- triangles

  1. Sep 30, 2004 #1
    ok, i'm in first year coolege and we're doing some review from highschool work.. but i can't for the life of me remember how to do one of these questions and i can't seem to get past this one part or at least figure out how to prove that it is what i think it is.

    it's gonna be a bit trickier, cuz i can't insert a picture, but i guess that isn't of the most importance anyways. alright

    you have triangle ABC.
    side AB=4 units
    side AC=7 units
    the line CD extends for 3 units towards point B, the distance between point B an D is unknown and is what needs to be found
    the Angle BCD is = angle DAC

    here's what i've tried to do so far...

    i've tried to fold the 2 triangles in half across the line AD, which lines up the two sides AB and AC, with the line AC extending 3 units futher then line AB. I'm still trying to follow this train of reasoning.. but so far with little success, i don't really know what to do next, but i think it helps somehow : )


    I tried extending the common side between the two triangles, line AD, far enough so that i can draw a new line, 7 units long, from point C, i'll call the intersection point E. The problem arises when i can't prove that the new triangle DEC is the same as triangle ADC. I CAN prove that it is proportional to triangle ABD, but that doesn't help me, because i only know that the side CE is 7 units, the Side DC is 3 units, and i don't know if i can prove that the angle DEC is equal to the angle DAC... which means i can't prove that the line DE is a continuation of the line AD...

    hence i'm lost.

    thx for the help in advance.. hey, kewl... just found the attacthment thing... i'll go draw a picture and then post :)

    Attached Files:

  2. jcsd
  3. Sep 30, 2004 #2
    Hint: angle bisector theorem.

    Hope that helps!
  4. Sep 30, 2004 #3
    nope, doesn't help... i looked it up on the net, and got this "The angle bisector of an angle in a triangle divides the opposite side in the same ratio as the sides adjacent to the angle."

    so the angle bisector is line AD, and the adjacent and opposiye side are? i can't assume ANY right angles... and all the other stuff i found on this theorem had something to do with area of a triangle, which i can't do either, because i don't have enough info to find that yet...

    a bit more of a hint is needed :confused:
  5. Oct 1, 2004 #4


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    No right angles required, merely an understanding of the words adjacent and opposite.

    Let me paraphrase the theorem for the triangle you've got :

    Simply, it says that CD/BD = AC/AB.

    Now go back and understand what the theorem is trying to say.
  6. Oct 1, 2004 #5
    so, 3/x=4/7
    huh, i had gotten that number before... just couldn't prove that it was the right number... now i can with that theorem

    thx a lot guys :)))))
  7. Oct 5, 2004 #6
    oops... i mean 3/7=x/4
    so 3/7=.429
    .429x4=1.7 units

    therefore BD=1.7
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