give example of Euclids 4th axiom
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This statement seems pretty vacuous: a right angle is a 90 degree angle, and obviously all 90 degree angles are equal. But we can understand Euclid's need for stating this fact when we consider that he didn't describe right angles in terms of degrees or any other angle measure (he didn't have one). Instead, he defined them in terms of a geometric picture: if two lines intersect, and the two angles formed by that intersection are equal, then that's your right angle.
Now suppose you have two angles that adhere to that definition of being right drawn on two separate bits of paper (or papyrus if you're Euclid). You might have a nagging suspicion that perhaps those two angles are different from each other. The fourth axiom says that they're not. Those right angles are in fact equal in the sense that you could move one of them on top of the other so that they perfectly align. Having established that fact Euclid could then go on to measure other angles in terms of right angles, for example by saying that a given angle is equal to three right angles.
Now suppose you have two angles that adhere to that definition of being right drawn on two separate bits of paper (or papyrus if you're Euclid). You might have a nagging suspicion that perhaps those two angles are different from each other. The fourth axiom says that they're not. Those right angles are in fact equal in the sense that you could move one of them on top of the other so that they perfectly align. Having established that fact Euclid could then go on to measure other angles in terms of right angles, for example by saying that a given angle is equal to three right angles.
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Euclid 's 4th Axiom - all right angles are equal.
A right angle is 90 degree angle and obviously all 90 degree angles are equal. But we can understand Euclid needs for stating this fact, when we consider that he didn't describe right angles in terms of degrees, or any other angle measure. But he defined them in terms of geometric pictures ie: if two lines intersect and the the angles formed by that intersection are equal, then that's your right angle.
A right angle is 90 degree angle and obviously all 90 degree angles are equal. But we can understand Euclid needs for stating this fact, when we consider that he didn't describe right angles in terms of degrees, or any other angle measure. But he defined them in terms of geometric pictures ie: if two lines intersect and the the angles formed by that intersection are equal, then that's your right angle.
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