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