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
c2 = a2 + b2
Examples :

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

1)

Solution :
By Pythagorean theorem

C2 = a2 + b2

x2 = 32 + 42

x2 = 9 + 16

x2 = 25

x = √25

x = 5

2)

Solution :
By Pythagorean theorem

c2 = a2 + b2

(45) 2 = (27) 2 + b2

2025 = 729 + b2

b2 = 2025 -729

b2 = 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,

c2 = a2 + b2

⇒ ( OB )2 = 102 + 242

= 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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