How to Learn Pythagorean Theorem

In the previous post we have discussed about Cones and In today's session we are going to discuss about Pythagorean Theorem, The Pythagorean Theorem is a theorem of the mathematics which establishes a relationship among all 3 sides in a right angled triangle. So let us discuss the statement of this theorem.
The Pythagorean Theorem states that in such a triangle which is right angled the area of a square the side of which is the hypotenuse of the right angled triangle that is the side which is opposite to the ninety degree angle is equal to the addition of the areas of those squares the sides of which are the 2 legs of the triangle that is those 2 sides which make the ninety degree angle. The Pythagorean Theorem is also sometimes known as the Pythagoras theorem.
The Pythagoras theorem can also be framed in a different way as follows. In a triangle which is right angled the square of the length of the hypotenuse of the right triangle is equal to the sum of the squares of the lengths of the other 2 sides of the right triangle that is the sides which make the ninety degree angle.
This theorem can also be represented in the mathematical way. Suppose that p, q and r are the lengths of the 3 sides of a right angled triangle then according to the Pythagoras theorem it can be given that,
p² + q² = r²
where r is the length of the hypotenuse and p & q are the lengths of the 2 sides which make the ninety degree angle. (want to Learn more about Pythagorean Theorem, click here),
The Pythagoras theorem can be proved by many different ways. For example this theorem can have the algebraic type of proofs and the geometric types of the proofs.
Linear equations solver makes your calculations easy and fun and linear equation is also an important topic of mathematics. icse board is a reputed board in India and provide quality education to students.

Pythagorean Theorem in Grade IX

Hello friends, in today's session we are going to learn about Pythagorean Theorem. The theorem gives a simple relation between the three sides of a right angle triangle.

According to the theorem, it states that:

In any Right Angle Triangle, the area of the square whose Side is the Hypotenuse is equal to the sum of the areas of the square whose sides are the two legs. In algebraic form the theorem can be written as: a² + b² =c², where a and b are the small sides and c is the hypotenuse of the right triangle.

In a right triangle if we know any two sides then we can easily find the other one with the Pythagoras equation.

If we generalize this theorem then we will get the law of cosines, which makes possible the computation of the third side of the triangle.

The converse of the theorem is also true:

For any three positive numbers a,b, and c such that a ² +b ² = c ², there exists a triangle with sides a,b and c, and every such triangle has a right angle between the sides of lengths a and b.

The Pythagoras equation is also used to find whether a triangle is acute, obtuse or right angle.

If a ² + b ² = c ², then the triangle is right angled.

If a ² + b ² > c ², then the triangle is acute angled.

If a ² + b ² < c ², then the triangle is obtuse angled.

Pythagorean triplet is a set of three positive integers a, b and c. These triplets satisfy the Pythagoras equation a ² + b ² = c ².

For example - (3, 4, 5), (5, 12, 13), (7, 24, 25), (8, 15, 17), (9, 40, 41), (11, 60, 61), (12, 35, 37) are some of the triplets below 100.

Now let's solve some examples based on Pythagoras theorem.

1. if two sides of the triangles are 5 and 12, then find the length of the hypotenuse?

By using Pythagoras theorem. a ² + b ² = c ². in here a = 5 and b = 12, so the value of c will be c ² = 25 + 144.

c ² = 169

c = 13.

2. if one side of the triangle is 9 and the hypotenuse is 15, then find the other side.

In this problem a = 9 and c= 15, then the third side will be b.

b ² = c ² - a ^2.

b ² = 225-81

b ² = 144

b = 12.

3. check whether the triangle with given sides is a right triangle or not. a = 10, b = 24 and c = 26.

We can check whether it is a right triangle or not by using the Pythagoras theorem.

26² = 10² + 24^2.

676 = 100 + 576.

676 = 676,

so these three sides satisfy the Pythagoras theorem, so the triangle formed will be right angled.