(Pythagoras’s Theorem) Prove by vector method that in a right angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

Question

Philoid · Accepted Answer

Given:- Right angle Triangle

To Prove:- Square of the hypotenuse is equal to the sum of the squares of the other two sides

Let ΔAOB be right angle triangle with right angle at O

Thus we have to prove

AB² = OA² + OB²

Proof: - Let, O at Origin, then

Since OB is perpendicular at OA

Therefore their Dot product is zero

)

⇒

⇒ ……(i)

Now,

⇒

From equation (i)

⇒

⇒ (Pythagoras theorem)

Hence, proved.