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.

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Pythagorean Theorem

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

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