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
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