The example below illustrates this calculation in Hyperbolic Geometry. If two parallels are cut by a transversal, the alternate interior angles are equal. In Euclidean Geometry, the area of a triangle is calculated by multiplying the length of any side times the corresponding height, and dividing the product by two (A½bh). Although non-Euclidean geometry may seem exotic and unfamiliar, it is actually. The sum of the angles of a triangle is two right angles. whether or not the square of the hypotenuse is equal to the square of the two sides). The hypotenuse of a right triangle is not always the shortest distance between the two points that define it. I recently encountered a Stack Overflow question (since closed) in which the OP was testing for whether a triangle was right by whether or not it "met" the criteria of the Pythagorean Theorem (i.e.
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