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Math Help - Obtuse angle is Right Angle

  1. #1
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    Obtuse angle is Right Angle

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    Last edited by Aquafina; June 10th 2009 at 05:54 AM.
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    Hello Aquafina
    Quote Originally Posted by Aquafina View Post
    hi i have the following question:

    this argument is given which makes an obtuse angle be a right angle, i have attached a picture of the shape.

    Given the obtuse angle x, we make a quadrilateral ABCD with ANGLE DAB = x, and ANGLE ABC =90◦, andAD = BC. Say the perpendicular bisector toDC meets the perpendicular bisector to AB at P. Then PA = PB andPC = PD. So the triangles PAD and PBC have equal sides and are congruent. Thus ANGLE PAD = ANGLE PBC. But PAB is isosceles, hence ANGLE PAB = ANGLE PBA.

    Subtracting, gives x = ANGLE PAD− ANGLE PAB = ANGLE PBC − ANGLE PBA = 90◦. This is a preposterous conclusion.

    Where is the mistake in the “proof” and why does the argument break down there?
    This is an interesting one. It shows that you can't rely on a diagram to tell the whole truth.

    In fact, if you draw the diagram carefully, you'll find that the line PD lies outside the quadrilateral - see the attached.

    You'll then find that instead of x = \angle PBC - \angle PBA, you get x = 360-(\angle PBC + \angle PBA), which is quite a different matter!

    Grandad
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    hi thanks thats exactly what i got, but wasnt sure if it was just the case in the way I was drawing it, and maybe if the line can come inside for certain lengths

    also, since it says that there is a mistake in the proof, can we assume that the mistake is not in the proof, but actually in the diagram, as an answer?
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  4. #4
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    Hello Aquafina
    Quote Originally Posted by Aquafina View Post
    hi thanks thats exactly what i got, but wasnt sure if it was just the case in the way I was drawing it, and maybe if the line can come inside for certain lengths

    also, since it says that there is a mistake in the proof, can we assume that the mistake is not in the proof, but actually in the diagram, as an answer?
    Clearly not - for if the line does come inside, there's nothing wrong with the proof. And clearly it is nonsense to conclude that x = 90^o. This is sufficient to tell you that the diagram cannot be drawn in this way.

    Grandad
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    thanks!

    do u have any ideas on this question that i posted earlier:

    http://www.mathhelpforum.com/math-he...-integers.html

    I was clueless on the 2nd bit..
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  6. #6
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    hi

    i need to say why the proof doesnt work because of the reason shown, i.e. it is drawn convectly?

    what can i say about this?
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