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 AC² = AB² + BC² 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).

2² = 4; 1² = 1; 1² = 1

1² + 1² = 2 ≠4
1² + 1² ≠ 2²

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).

50² = 2500 14² = 196 48² = 2304

14² + 48² = 196 + 2304 = 2500

14² + 48² = 50²

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 90⁰ ?

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

61² = 3721

11² = 121 60² = 3600

11² + 60² = 121 + 3600 = 3721

11² + 60² = 61²

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

As AC is the hypotenuse so ∠B = 90⁰

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Pythagorean Theorem

• Introduction of Pythagorean Theorem
• Converse of Pythagorean Theorem
• Pythagorean Triples
• Application of Pythagorean Theorem
• Proof on Pythagorean Theorem

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