# Converse of Pythagorean Theorem

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**Converse of Pythagorean theorem states that : If the square of one side of a triangle is equal to the sum of the squares of the other two sides, then the angle opposite the first side is a right angle and so the triangle is right angled triangle.**

If AC

^{2}= AB

^{2}+ BC

^{2}then ∠C is the angle and ΔABC is a right angled triangle.

**Examples**

Q.1 Find which of the following are sides of a right triangle.

i) 1,1,2

**Solution :**

Here the 2 is the largest number so 2 must be a longest side(may be hypotenuse).

2

^{2}= 4; 1

^{2}= 1; 1

^{2}= 1

1

^{2}+ 1

^{2}= 2 ≠4

1

^{2}+ 1

^{2}≠ 2

^{2}

So, 1,1,2 are not the sides of right triangle.

ii) 14,48,50

**Solution :**

Here the 50 is the largest number so 50 must be a longest side (may be hypotenuse).

50

^{2}= 2500 14

^{2}= 196 48

^{2}= 2304

14

^{2}+ 48

^{2}= 196 + 2304 = 2500

14

^{2}+ 48

^{2}= 50

^{2}

So, 14,48,50 are the sides of right triangle.

iii) In a triangle ABC, AB = 11cm, BC = 60 cm and AC = 61 cm. Examine if ΔABC is a right triangle. If yes,which angle is equal to 90

^{0}?

**Solution :**

Here the 61 is the largest number so 61 must be a longest side(may be hypotenuse).

61

^{2}= 3721

11

^{2}= 121 60

^{2}= 3600

11

^{2}+ 60

^{2}= 121 + 3600 = 3721

11

^{2}+ 60

^{2}= 61

^{2}

So, 11,60,61 are the sides of right triangle.

As AC is the hypotenuse so ∠B = 90

^{0}

**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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