What is the difference between the Pythagorean Theorem and the converse of the Pythagorean Theorem?

The Pythagorean theorem is used to find the length of a missing side of a right triangle, the converse of the Pythagorean Theorem is used to determine if a triangle is a right triangle or not.

What theorem states that the square of the hypotenuse is equal to the sum of the squares of the legs?

Pythagorean theorem
Pythagorean theorem, the well-known geometric theorem that the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse (the side opposite the right angle)—or, in familiar algebraic notation, a2 + b2 = c2.

Why does the Pythagorean Theorem work?

Pythagoras’ theorem enables construction of incommensurable lengths because the hypotenuse of a triangle is related to the sides by the square root operation. The figure on the right shows how to construct line segments whose lengths are in the ratio of the square root of any positive integer.

Why is the converse of the Pythagorean Theorem important?

The converse of the Pythagorean Theorem enables them to do just this: they can conclude that an angle is a right angle provided a certain relationship holds between side lengths of a triangle.

What does converse mean in Pythagorean Theorem?

The converse of the Pythagorean Theorem is: If the square of the length of the longest side of a triangle is equal to the sum of the squares of the other two sides, then the triangle is a right triangle.

Why does the Pythagorean theorem need to be squared?

The squares are required because it’s secretly a theorem about area, as illustrated by the picture proofs you’ve mentioned. Since a side length is a length (obviously), when you square it you get an area.

How do you find out if a triangle is acute obtuse or right with side lengths?

Classifying Triangles You can determine whether a triangle is acute, right, or obtuse by its side lengths. In TABC with longest side c: If c2 a2 b2, then TABC is acute. If c2 a2 b2, then TABC is right.

Why is the Pythagorean Theorem not a law?

Why is the Pythagorean Theorem not a law? Because breaking it should not be a criminal offence. If the Pythagorean theorem were a law, you wouldn’t be able to break it, but it is not true in all geometries, so you can. In fact it is only true in Euclidean geometry (in two or more dimensions).