# Obtuse angle is Right Angle

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• May 4th 2009, 04:26 AM
Aquafina
Obtuse angle is Right Angle
on another thread
• May 5th 2009, 02:01 AM
Grandad
Hello Aquafina
Quote:

Originally Posted by Aquafina
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
• May 5th 2009, 04:11 AM
Aquafina
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?
• May 5th 2009, 10:44 AM
Grandad
Hello Aquafina
Quote:

Originally Posted by Aquafina
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
• May 5th 2009, 11:08 AM
Aquafina
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..
• May 9th 2009, 05:41 AM
Aquafina
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?