An it is intended triangle whose next lengths are equal to 1. Observe that in this certain case, $a^2+b^2 eq c^2$. Describe why this doesn"t violate the Pythagoras" Theorem.

You are watching: Does pythagorean theorem work on equilateral triangles

I"m stuck with this exercise. Give some advice what I need to check before trying to answer this question.

Is there any exception because that equilateral triangles because of side lengths equality?


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When other violates one estabilished theorem, the reason is constantly that it doesn"t respect the hypothesis. So, what go Pythagoras" organize say?

From Wikipedia

In benidormclubdeportivo.orgematics, the Pythagorean theorem, likewise known as Pythagoras"s theorem, is a relation in Euclidean geometry among the 3 sides of a ideal triangle. It says that the square of the hypotenuse (the side opposite the right angle) is same to the amount of the squares of the other two sides.

What is the hypothesis? Well, simply one fact: "we space in a appropriate triangle". For this reason you need to ask yourself: am ns in a ideal triangle?


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All answers are ok, yet on a sphere of radius $frac2pi$, you can have an equilateral triangle of sides $1$ through 3 right angles.

But the Pythagorean theorem only uses in euclidean geometry, no in spherical geometry.

So you might violate one or one more hypothesis (this answer is just to illustrate that "a best angle" is not the just hypothesis of this theorem)


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$a^2 + b^2 = c^2$ is just true in the situation of a best triangle (with one edge of the triangle gift 90 degrees). Due to the fact that you are working with an it is provided triangle, all angle of the triangle room 60 degrees and also thus, you perform not have a appropriate triangle.

In such a case where you know you have an it is provided triangle and you desire to know any kind of angles or sides, the legislation of cosines (a more general kind of the Pythagorean theorem) or the law of sines would certainly work.


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