Converse of Pythagorean Theorem

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

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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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