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Hi guys I just need to know if my answer is right.

The question is

1) Euclids $4^{th}$ postulate is "That all right angles are equal to one another". Why is this not obvious?

My answer:

When I read this question I am like it is obvious, so I got kind of confused. But I took a crack at it anyways.

If you read the postulate. This is not obvious because you dont know if the right angle is a right angle. What if a triangle was drawn differently but with one line perpendicular to another. You need to know if the line is perpendicular or not, and that is why it is not obvious.

Could someone tell me if that is right or should I add in more info.

MathGeek
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1 Answers1

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Euclid did not think of angles in terms of numeric measures (such as 90 degrees). Instead, he compared angles to one another by properties.... The three angles of any right triangle are equal to two right angles, for example. So my interpretation of the 4th axiom is that Euclid needed a standard with which to compare all other angles. In other words, there could be a fixed right angle $R$, and thus any triangle whatsoever has three angles that equal twice the measure of $R$ (for example).

Hope this helps!

Shaun Ault
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  • yes it did, so thats what I was confused I know its 90 degrees. SO in his case he didnt know? so he actually check it out by his axioms to say if it was a right angle or not then right – MathGeek Apr 15 '13 at 10:24
  • It's just that Euclid never attached a number to angle measurement the way we do today. His approach was only to argue about and compare the geometric objects themselves. Here's a really short blurb about that: http://aleph0.clarku.edu/~djoyce/java/elements/bookI/defI9.html – Shaun Ault Apr 15 '13 at 11:52