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Thread: Triangle inequality challenge

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    Triangle inequality challenge

    Triangle inequality challenge-38.png
    I am supposed to do this without using the Pythagorean Triples because we're not up to that chapter yet. The back of my text says that Angle 2 is greater than Angle X. Help is much appreciated!
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    Re: Triangle inequality challenge

    Quote Originally Posted by lamp23 View Post
    Click image for larger version. 

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    I am supposed to do this without using the Pythagorean Triples because we're not up to that chapter yet. The back of my text says that Angle 2 is greater than Angle X. Help is much appreciated!
    I not sure what is expected of you in terms of reasoning.
    There is a theorem that says: In a triangle the measure of corresponds to the measure of the opposite side. In other words, the longest side is opposite the largest angle.
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    Re: Triangle inequality challenge

    Quote Originally Posted by Plato View Post
    I not sure what is expected of you in terms of reasoning.
    There is a theorem that says: In a triangle the measure of corresponds to the measure of the opposite side. In other words, the longest side is opposite the largest angle.
    I am given that and the converse and I know how to use that on each individual triangle but I do not know how to figure out that Angle 2 is greater than Angle X because they are not in the same triangle.
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    Re: Triangle inequality challenge

    Quote Originally Posted by lamp23 View Post
    I am given that and the converse and I know how to use that on each individual triangle but I do not know how to figure out that Angle 2 is greater than Angle X because they are not in the same triangle.
    m(\angle 2) = m(\angle X) + m(\angle XZW)>m(\angle X)

    WHY is that the case?
    Thanks from lamp23
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    Re: Triangle inequality challenge

    Quote Originally Posted by Plato View Post
    m(\angle 2) = m(\angle X) + m(\angle XZW)>m(\angle X)

    WHY is that the case?
    The exterior angle theorem. Thanks!
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    Re: Triangle inequality challenge

    That turned on your lamp
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