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Math Help - Triangle

  1. #1
    Junior Member whytechocolate01's Avatar
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    Triangle

    What postulate or theorem justifies the statement..Triangle ABC is similar to Triangle RST...

    Pweez sumone explainz!
    Attached Thumbnails Attached Thumbnails Triangle-similar.jpg  
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    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by whytechocolate01 View Post
    What postulate or theorem justifies the statement..Triangle ABC is similar to Triangle RST...

    Pweez sumone explainz!
    two triangles are said to be similar if:
    1) corresponding angles are equal
    2) the ratio of corresponding sides are equal

    the second posulate is what justifies the statement that these triangles are similar.

    we see that side rs of one triangle corresponds to side ab of the other, and side st of one triangle corresponds to side bc of the other.

    if these triangles are similar, then, for example:

    rs/st = ab/bc

    now, rs/st = 5/6

    and ab/bc = 10/12 = 5/6 = rs/st

    thus the triangles are similar
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  3. #3
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by whytechocolate01 View Post
    What postulate or theorem justifies the statement..Triangle ABC is similar to Triangle RST...

    Pweez sumone explainz!
    I don't really understand this question. From the given information we cannot say if these two triangles are similar or not because we have no information about the third side and don't know any of the angles.

    IF the ratio of the lengths of sides rt/ac = 5/10 = 6/12 or IF angles s and b are equal then we may say that the two triangles are similar.

    -Dan
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    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by topsquark View Post
    I don't really understand this question. From the given information we cannot say if these two triangles are similar or not because we have no information about the third side and don't know any of the angles.

    IF the ratio of the lengths of sides rt/ac = 5/10 = 6/12 or IF angles s and b are equal then we may say that the two triangles are similar.

    -Dan
    if we have two sides proportional, can we not assume that the third side is proportional as well

    can you come up with a counter-example for such an assumption?
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  5. #5
    Bar0n janvdl's Avatar
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    Quote Originally Posted by whytechocolate01 View Post
    What postulate or theorem justifies the statement..Triangle ABC is similar to Triangle RST...

    Pweez sumone explainz!
    The first 2 sides are equal with an enlargement value of two.
    So the third side will also be equal.

    To prove this theorem takes a little bit more...

    We first have to construct a triangle the size of the little one inside the bigger one.

    Then prove them congruent.

    Then we must prove their angles equal, which is relatively easy.

    If you want me to thoroughly explain it to you, just ask and i'll be happy to do it.
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  6. #6
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by Jhevon View Post
    if we have two sides proportional, can we not assume that the third side is proportional as well

    can you come up with a counter-example for such an assumption?
    Quote Originally Posted by janvdl View Post
    The first 2 sides are equal with an enlargement value of two.
    So the third side will also be equal.
    I disagree. We may construct two triangles, one with angle s equal, say, to 30 degrees, and angle b equal to 25 degrees.
    Then: rt = sqrt{5^2 + 6^2 + 2*5*6*cos(30)} = 10.6283
    Then ac = sqrt{10^2 + 12^2 + 2*10*12*cos(25)} = 21.4829

    and rt/ac = 0.494735
    which is not the required 1/2.

    -Dan
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  7. #7
    Bar0n janvdl's Avatar
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    If the 1st two sides are proportional, then the 3rd side MUST be proportional. I cannot see any other way.
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  8. #8
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    Quote Originally Posted by janvdl View Post
    If the 1st two sides are proportional, then the 3rd side MUST be proportional. I cannot see any other way.
    Hi,

    I have attached a diagram to illustrate your statement. As you may see the ratios between corresponding sides are equal but they are not similar.
    Attached Thumbnails Attached Thumbnails Triangle-selbes_verhaeltnis.gif  
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  9. #9
    Bar0n janvdl's Avatar
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    How do u know that the other 2 sides arent proportional?

    Could someone please prove this? It seems i've been taught wrong all this time...
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  10. #10
    Forum Admin topsquark's Avatar
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    Two triangles are similar if they have the same angles, or if ALL of the sides are in the same proportions to each other. We don't have enough information from either triangle to state what any of the angles are, and we don't have enough information to calculate that third side, so we can't say they are similar.

    This is almost a trick question. The diagrams that are given are drawn to show that the angles are the same, which is meant to throw you off. NEVER trust the way a sketch looks, depend only on the numbers.

    -Dan
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