LEARN MATH STEP BY STEP THROUGH VERY EASY PROCESS

PYTHAGORAS' THEOREM

__PYTHAGORAS’ Theorem –__

**Pythagoras was a Greek mathematician who
came up with a relation between the areas of the squares (constructed) on the
sides of a right-angled triangle. He figured out that the square on the
hypotenuse is equal to the sum of the squares on the other two sides. In the figure, this would mean
AC² = AB² + BC², since the area of a square is the square of its side. So, Pythagoras’ theorem, as the relation is called, is a relation between the sides of a right-angled
triangle as well.**

**The converse of the theorem is also true. That means if the square on one side of a triangle is equal to the sum
of the squares on the other two sides then those two sides contain a right-angle
and the triangle is a right-angled triangle. To put it simply, if an ∆ ABC is
such that AC²= AB²+ BC², then ∠B = 90⁰
and ∆ ABC is right angled.**

**Example)
Calculate the length of the unknown side in each of the following triangles**

**Ans.) As per the Pythagoras theorem AC²= BC²+ AB²**

**As per the above given picture
AB = 15 cm and BC =
20 cm**

**So, AC² = 20² + 15² = 400 + 225 = 625**

**Or, AC = √625 = √25² =
25 (Ans.)**