Q: Why does Pythagoreans theorem work for right triangles?

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It doesn't matter on the side length, but it MUST have a right angle.

An equilateral triangle has all 3 sides the same length. To find the height of a triangle, draw a line from the tip top of the triangle to the middle of the base. You should see 2 triangles now inside your original triangle. We can use Pythagoras' theorem to figure out the length of this line, the height. This theorem will only work with right triangles, which (luckily) we have just created by drawing the height line inside the triangle. The P. theorem says that side squared + side squared = hypotenuse squared. Our hypotenuse is the left or right side of the original triangle, 6 cm. The line we drew down the center is one side, and HALF of the base is the other side for the P. theorem, since the height line of the triangle cuts the base exactly in half, and creates 2 right angles at the base. This line also creates 2 right triangles inside. This is why we can use the P. theorem to help us! But we'll only be using 1 of the inside triangles. (Even though, both are identical) side squared + side squared = hyp. squared (3 cm) squared + ??? squared = 6 squared 9 + ??? squared = 36 ??? squared = 36 - 9 ??? squared = 27 ??? = sqrt(27) We can simplify sqrt(27), or you can use a calculator to approximate it. sqrt(27) = sqrt(9*3) = 3 * sqrt(3)

It works in Euclidean geometry, but not in hyperbolic.

It is the longest distance between two opposite corners of the square and it is possible to use Pythagoras' theorem to find the length of the diagonal

If needed, I guess. I do not see lawyers needing the Pythagorean Theory in their work and lawyers are notoriously ignorant of math and science.

Related questions

no only right triangles

No, only right triangles

No, the pythagorean theorem only works on right triangles, but it will work on any right triangle. This is because the Pythagorean Theorem states that length of Leg A squared plus the length of Leg B Squared equals the length of the hypotenuse squared. A hypotenuse is always found opposite a right angle. Only right triangles have right angles; therefore, the Pythagorean Theorem only applies to right triangles. :D

It doesn't matter on the side length, but it MUST have a right angle.

All right-angles triangles. That is triangles that contain one angle at 90 degrees.

anyone doing work with right angled triangles

it depens if the isosceles triangle is a right triangle or not

I quote " The square on the hypotenuse of a rightangled triangle..."

Pythagoras invented the Pythagorean Theorem of course, but it only can work for right triangles, not any other triangle. The formula is- A2+B2=C2

Yes, all plane triangle.

When trying to prove two triangles congruent, you can use SSS, SAS, ASA, AAS, HL, and HA patterns. However, the pattern A S S doesn't work. Instead of spelling or saying this word in class, you can refer to it as "the donkey theorem". You can look at the pattern in the two triangles and say "these two triangles are not congruent because of the donkey theorem." You CANNOT prove triangles incongruent with 'the donkey theorem', nor can you prove them congruent. It's mostly sort of a joke, you could say, but it's never useful. The reason is that if the two triangles ARE congruent, then of course there will be an unincluded congruent angle as well as two congruent sides. The theorem doesn't do anything left, right, forward or backward. It's not even really a theorem. :P

It does not; if there is no 90 degree angle there is no hypotenuse.