Geometry: Understanding the Pythagoras Theorem

Years ago, a mathematician namely Pythagoras stated a theorem on right angles triangles. Hence the theorem is named as Pythagoras theorem. Pythagoras theorem states that “In a right angled triangle, the square of length of the hypotenuse (the longest side) is the sum of the squares of the other two sides.

By Pythagoras theorem,

c2 = a2+b2

where c is the hypotenuse and a,b are the legs of the right angle triangle.

This means that, if we frame the squares along all the three sides of a right angled triangle then the area of square along hypotenuse is equal to the areas of the other two squares put together.

Example:

Here 52 = 32 + 42

25 = 9+16

25=25.

So, Pythagoras theorem is used to determine whether the given triangle is right-angled.

Since here we got 25=25 using the statement of Pythagoras theorem, we can say that the triangle with lengths 3,4 and 5 is right-angled.

Also, Pythagoras theorem is used to determine the length of an unknown side of a right angled triangle.

Example:

By Pythagoras theorem,

a2 + 42 = 52

a2 + 16 = 25

a2 = 25-16=9

a = √9=3

In the same way, Pythagoras theorem is used to obtain the formula for the diagonal of a square.

Since all the angles in square are right angles, Pythagoras theorem can be applicable for the triangle which is inside the square.

So, diagonal2 = a2 +a2=2a2

So, the diagonal of square = √2 a

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