Question 438893
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In an isosceles right triangle (45 - 45 - 90), if *[tex \Large x] represents the measure of either leg, then *[tex \Large x\sqrt{2}] represents the length of the hypotenuse.


Proof:


Let *[tex \Large x] represent the length of one leg and let *[tex \Large h] represent the measure of the hypotenuse.


Then *[tex \Large h^2\ =\ x^2\ +\ x^2] by the Pythagorean theorem.


Collect terms and take the square root of both sides:  *[tex \Large h\ =\ \sqrt{2x^2}\ =\ x\sqrt{2}]


QED.


John
*[tex \LARGE e^{i\pi} + 1 = 0]
My calculator said it, I believe it, that settles it
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