Sage-Tips

Can the hypotenuse be equal to a leg in a right triangle?

No, it can’t. The largest angle in a right triangle is 90 degrees and it is the largest angle of the triangle. The side opposite the largest angle has to be the largest side.

How can we disprove the Pythagorean theorem?

If the square is a units on each side, each leg of the triangle that makes up a quarter of the square will be a/√2. Big Gus said: Try an example lets say a=4 b=5 and by the Pythagorean theorem c=5 but by the formula c^2=2ab c=sqrt20..

Are there exceptions to the Pythagorean theorem?

A theorem about right triangles must be true for every right triangle; there can be no exceptions. Just showing that an idea works in several cases is not enough to make an idea into a theorem. The Pythagorean theorem has been proven to work for every possible right triangle.

Is Pythagorean theorem only for hypotenuse?

Note that the Pythagorean Theorem only works with right triangles. You can use the Pythagorean Theorem to find the length of the hypotenuse of a right triangle if you know the length of the triangle’s other two sides, called the legs.

What is the hypotenuse leg of a triangle?

In a right-angled triangle, the hypotenuse is the longest side which is always opposite to the right angle. The hypotenuse leg theorem states that two right triangles are congruent if the hypotenuse and one leg of one right triangle are congruent to the other right triangle’s hypotenuse and leg side.

Is hypotenuse greater than legs?

Since a right angle is half that (90°), it has to be the biggest angle in the triangle and the side across from it will always be the longest. …

Who proved the Pythagorean Theorem?

Euclid was the first to mention and prove Book I, Proposition 47, also known as I 47 or Euclid I 47. This is probably the most famous of all the proofs of the Pythagorean proposition.

Is the Pythagorean theorem valid?

It is not. It is a statement about the relationship between the lengths of the sides of a mathematical concept known as a right triangle. And the Pythagorean theorem is a mathematical theorem, not a scientific hypothesis.

How do you find the legs of a triangle with only the hypotenuse?

You can multiply the short side by the square root of 3 to find the long leg. Type 2: You know the hypotenuse. Divide the hypotenuse by 2 to find the short side. Multiply this answer by the square root of 3 to find the long leg.

What is hyphypotenuse leg theorem?

Hypotenuse Leg Theorem In a right-angled triangle, the hypotenuse is the longest side which is always opposite to the right angle. The hypotenuse leg theorem states that two right triangles are congruent if the hypotenuse and one leg of one right triangle are congruent to the other right triangle’s hypotenuse and leg side.

What is the hypotenuse of a right triangle?

In a right-angled triangle, the hypotenuse is the longest side which is always opposite to the right angle. The hypotenuse leg theorem states that two right triangles are congruent if the hypotenuse and one leg of one right triangle are congruent to the other right triangle’s hypotenuse and leg side.

How to prove any two right triangles are congruent?

In order to prove any two right triangles congruent, we apply the HL (Hypotenuse Leg) Theorem or the RHS (Right angle-Hypotenuse-Side) congruence rule. Let us learn more about the hypotenuse leg theorem in this page. 1. 2. 3. 4. 5.