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Math Help - Finding the length of a side of a triangle:

  1. #1
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    Finding the length of a side of a triangle:


    In the above triangle ABC, line segment AD is 6, and I'm supposed to find the length of side BC.

    I know I'm missing some basic knowledge about properties of triangles, or else this wouldn't completely baffle me.

    Any help would be greatly appreciated.
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  2. #2
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    Quote Originally Posted by thumpin_termis View Post

    In the above triangle ABC, line segment AD is 6, and I'm supposed to find the length of side BC.
    ...
    Hello,

    I've modified your drawing a little bit so you can see how I did this problem:

    (< this sign means angle):

    <(CDB) = 2x ==> <(ABD) = x

    Therefore triangle BAD is an isoscele triangle with the base AB. Thus AD = DB.

    Triangle DCB is an isoscele triangle with the base DC. Thus DB = BC.

    That means: 6 = AD = DB = BC
    Attached Thumbnails Attached Thumbnails Finding the length of a side of a triangle:-anlieg_aussenwinkl.gif  
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  3. #3
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    Hello, thumpin_termis!

    Earboth is absolutely correct.
    . . Here's the reason behind his solution.

    Angle BDC = 2x is an exterior angle of triangle ABD.
    . . Hence, it is the sum of the two non-adjacent angles.

    That is: ./BDC .= ./BAD + /ABD

    Hence: . . . 2x .= .x + /ABD

    Then: . . /ABD .= .x


    Therefore, triangle ABD is isosceles, BD = AD = 6, etc.

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  4. #4
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    Awesome.

    So lemme just make sure here:
    /ABD = x can be found from the original information given, since /BDC=./BAD + /ABD would be true in such situations. Did I get that right?
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  5. #5
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    Quote Originally Posted by thumpin_termis View Post
    Awesome.

    So lemme just make sure here:
    /ABD = x can be found from the original information given, since /BDC=./BAD + /ABD would be true in such situations. Did I get that right?
    Hello,

    you got it.

    Have a look at Soroban's post.
    The exterior angle of a triangle is as great as the two non-adjacent angles of the triangle.

    You can proof this "theorem" by using that the 3 angles in a triangle sum up to 180 and that a straight line forms an angle of 180 too.
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  6. #6
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    Fantastic. Thank you very much guys.
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  7. #7
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    Quote Originally Posted by CaptainBlack View Post
    There is insufficient information. The diagram looks like AD=DB but you
    cant assume that, it must state it.

    RonL
    angle 2x (D) = angle x (A) + angle () B .......... property of external angle to triangle
    hence angle B = x
    hence side AD = Side BD
    Similarly angle BDC = Angle BCD
    hence side BD = Side BC = 6
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