Its a special relationship that was observed by Pythogorous. It just kind of works
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)
No, two equilateral triangles do not make a square. A square has four equal sides and four right angles, while an equilateral triangle has three equal sides but three angles that add up to 180 degrees. When two equilateral triangles are put together, they do not form a shape with four equal sides and four right angles, which is the defining characteristic of a square.
It works in Euclidean geometry, but not in hyperbolic.
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.
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
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
It doesn't matter on the side length, but it MUST have a right angle.
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
The Pythagorean theorem applies specifically to right triangles because it defines a relationship between the lengths of the sides in a triangle where one angle is exactly 90 degrees. In this configuration, the lengths of the two legs (the sides forming the right angle) can be squared and summed to equal the square of the length of the hypotenuse (the side opposite the right angle). For triangles without a right angle, this relationship does not hold, as the properties of triangle geometry change, and the sum of the squares of the sides does not equal the square of the longest side. Thus, the theorem is uniquely suited to right triangles.
The Pythagorean theorem only applies to right triangles, where one angle measures 90 degrees. It states that the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides. For triangles that are not right triangles, different formulas, such as the Law of Cosines, must be used to relate the sides and angles.
Yes, all plane triangle.