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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