## WHAT IF A squared plus B squared is greater than c squared?

Pythagoras’s theorem states that, in any right-angled triangle, π΄ squared plus π΅ squared is equal to πΆ squared, where πΆ is the longest side of the triangle, known as the hypotenuse. We can therefore say that when angle πΆ is obtuse, π΄π΅ squared is greater than π΅πΆ squared plus π΄πΆ squared.

## When A squared plus B squared is less than c squared?

And the right angle is opposite our π, which is our longest side. And then we have the relationship which is that if π squared plus π squared is less than π squared, then actually we’re gonna have an obtuse triangle. And that means that the angle opposite our longest side is going to be obtuse.

**What does Pythagoras famous theorem involve?**

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)βor, in familiar algebraic notation, a2 + b2 = c2.

**What is Thales theorem converse?**

One way of formulating Thales’s theorem is: if the center of a triangle’s circumcircle lies on the triangle then the triangle is right, and the center of its circumcircle lies on its hypotenuse. The converse of Thales’s theorem is then: the center of the circumcircle of a right triangle lies on its hypotenuse.

### What if the square of the longest side is less than the sum of the squares of the shorter side?

This means the longest side of the triangle lies opposite of the 90 degree or right angle. The angle formed by the two sides must be less than 90 degrees. If the sum of the squares of the shorter sides is smaller than the square of the longest side, then the triangle is an obtuse triangle.

### How Pythagorean Theorem changed the world?

The Pythagoras’ theorem has changed. For the past 2500 years, the Pythagoras’ theorem, arguably the most well-known theorem in the world, has greatly helped mankind to evolve. Its useful right angles are everywhere, whether it is a building, a table, a graph with axes, or the atomic structure of a crystal.

**How did Pythagoras come up with the Pythagorean Theorem?**

The legend tells that Pythagoras was looking at the square tiles of Samos’ palace, waiting to be received by Polycrates, when he noticed that if one divides diagonally one of those squares, it turns out that the two halves are right triangles (whose area is half the area of the tile).

**How do I find my Toa?**

CAH: Cos(ΞΈ) = Adjacent / Hypotenuse. TOA: Tan(ΞΈ) = Opposite / Adjacent.

#### Can you use Sohcahtoa on non right triangles?

For right-angled triangles, we have Pythagoras’ Theorem and SOHCAHTOA. However, these methods do not work for non-right angled triangles. For non-right angled triangles, we have the cosine rule, the sine rule and a new expression for finding area.