# Introduction of Pythagorean Theorem

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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 + 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

• Introduction of Pythagorean Theorem

• Converse of Pythagorean Theorem

• Pythagorean Triples

• Application of Pythagorean Theorem

• Proof on Pythagorean Theorem

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