![Pythagorean](http://blogs.scientificamerican.com/roots-of-unity/files/2014/04/Pythagorean.jpg)
An illustration from Oliver Byrne’s 1847 edition of Euclid’s Elements. Euclid’s fourth postulate states that all the right angles in this diagram are congruent. Image: Public domain, via Wikimedia Commons.
Why the heck do we need a postulate that says that all right angles are equal to one another? You probably remember learning in a middle or high school geometry class that right angles are 90 degree angles, and two angles are congruent if they have the same degree measure. We don’t need a whole postulate that says this. It’s just part of the way we define angles. Why not a postulate that says that all 45 degree angles are equal to one another? Or all 12 degree angles? The fourth postulate seems a bit bizarre. But Euclid knew what he was doing, so there must be a reason for this postulate.
Read the full post at Roots of Unity.
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