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.
Q.1 Find which of the following are sides of a right triangle.
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.
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 ?
Here the 61 is the largest number so 61 must be a longest side(may be hypotenuse).