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


Pythagorean Theorem

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

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