# 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 )

( AB )

c

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

1)

By Pythagorean theorem

C

x

x

x

x = √25

x = 5

2)

By Pythagorean theorem

c

(45)

2025 = 729 + b

b

b

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.

By Pythagorean theorem,

c

⇒ ( OB )

= 100 + 576

= 676

( OB)

∴ OB = √676

∴ OB = 26 cm.

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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 + 16x

^{2}= 25x = √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 -729b

^{2}= 1296b = √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

• Introduction of Pythagorean Theorem

• Converse of Pythagorean Theorem

• Pythagorean Triples

• Application of Pythagorean Theorem

• Proof on Pythagorean Theorem