Question

prove at least any one please tommorow I have half yearly

Answer 1

If the square of the length of the longest side of a triangle is equal to the sum of the squares of the other two sides, then the triangle is a right triangle.

GIven a ΔABC, with BC = a, AC = b and AB = c.

Also given, c2 = a2 + b2  --- (1)

Now construct a right angled ΔDEF, with sides EF = BC = a, AC = DF = b.

Let DE = d and ∠EFD = 900

SInce, ΔDEF is a right angled triangle, we can use Pythagoras theorem,  

⇒ d2 = a2 + b2

But by (1),  c2 = a2 + b2  

Therefore, c = d

i.e. AB = DE  

Thus, by construction , By SSS test, ΔABC ≃ ΔDEF  

Thus, ΔABC is a right angled triangle with ∠ACB = 900.