Question

main topic of Pythagorean theoram​

Answer 1

$\;\large{\odot\;\;\underline{\underline{\bf{Pythagoras\;\;Theorem}}}}$

• Definition :

Pythogoras Theorem states that in a right angled triangle, the square of Hypotenuse is equal to the sum of squares of its Base and Height.

• Converse of Pythagoras Theorem :

This is just the converse and derivative of Pythagoras Theorem. It states that if the square of Hypotenuse is equal to the sum of squares of its Base and Height, thenthe triangle is Right Angled Triangle.

This theorem can be formulated as,

$\;\large{\boxed{\bf{\purple{(Hypotenuse)^{2}\;=\;(Base)^{2}\;+\;(Height)^{2}}}}}$

From this main formula, we can derive that

$\;\bf{\green{\rightarrow\;\;(Hypotenuse)^{2}\;-\;(Base)^{2}\;=\;(Height)^{2}}}$

$\;\bf{\green{\rightarrow\;\;(Hypotenuse)^{2}\;-\;(Height)^{2}\;=\;(Base)^{2}}}$

The figure shown in the attachment I depicts a right triangle.

• Main points regarding Pythagoras Theorem :

• It is applicable to only Right - Triangles.

• The formula of Pythagoras Theorem is justified to only cases where the longest side is hypotenuse.

• For a right triangle, length of hypotenuse should be smaller than the sum of other two sides.

• To prove if a given triangle is right triangle or not, we can verify using Pythagoras Theorem. If the condition satisfies, then the give triangle is right angle triangle and others are either base or height.

• From the given sides of a right triangle, hypotenuse should be longest in length from others.

• It tells the relationship between the sides of right angled triangle.

• Hypotenuse is the side opposite to the right angle and between the vertex of base and height.

• Base is one of the side containing right angle is the planar line which shows the side on which triangle is there.

• Height is the second side containing right angle which is the altitude of the triangle.

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★ More to know :-

• About Pythagoras :: He was a Ionian greek philosopher of Samos between the years of 570 BC - 495 BC and was the founder of Pythagoreanism. Please refer the second attachment to see a image showing Pythagoras depicting an experiment with a right prism. He was well know for his Pythagoras Theorem.

• Trigonometry :: It is a branch of mathematics which deals with measure of sides of a Triangle. Like Pythagoras Theorem, trigonometry is applicable for only right angled triangles.

Answer 2

Pythagoras theorem states that “In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides“. ... The sides of a right triangle (say a, b and c) which have positive integer values, when squared, are put into an equation, also called a Pythagorean triple.