Introduction of Pythagorean Theorem

In this section we will discuss about the introduction of Pythagorean theorem.

A right angled triangle has one right angle and two acute angles. The side opposite to the right angle is called the
hypotenuse . The other two sides are called its legs. According to the right triangle hypotenuse is the longest side than the legs. In a right angled triangle, the sides which contain the right angle are usually referred to as the base and perpendicular.


Pythagorean theorem : It states that the square of hypotenuse is equal to the sum of the squares of other two legs.

(Hypotenuse )
2 = (base ) 2 + ( Perpendicular ) 2
( AB )
2 = ( BC ) 2 + ( AC ) 2
c
2 = a 2 + b 2
Examples :

Q.1 Find the missing sides of the triangle using Pythagorean theorem.

1)

Solution :
By Pythagorean theorem

C
2 = a 2 + b 2

x
2 = 3 2 + 4 2

x
2 = 9 + 16

x
2 = 25

x = √25

x = 5

2)

Solution :
By Pythagorean theorem

c
2 = a 2 + b 2

(45)
2 = (27) 2 + b 2

2025 = 729 + b
2

b
2 = 2025 -729

b
2 = 1296

b = √1296

b = 36

3) A man goes 10 m due East and then 24 m due North. Find the distance from the starting point.

Solution :

By Pythagorean theorem,

c
2 = a 2 + b 2

⇒ ( OB )
2 = 10 2 + 24 2

= 100 + 576

= 676

( OB)
2 = 676

∴ OB = √676
∴ OB = 26 cm.

Pythagorean Theorem

Introduction of Pythagorean Theorem
Converse of Pythagorean Theorem
Pythagorean Triples
Application of Pythagorean Theorem
Proof on Pythagorean Theorem

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