# Thread: Obtuse angle is Right Angle

1. ## Obtuse angle is Right Angle

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2. Hello Aquafina
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

3. 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?

4. Hello Aquafina
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

5. 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..

6. 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?

### how to prove obtuse angle is a right angle

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