Question

state and prove pythagoras theorem

Answer 1

Pythagoras Theorem:- In a right angled triangle, the square of length of hypotenuse is equal to the sum of squares of lengths of other two sides.

Data:- In ΔABC, m∠B=90
To prove:- AC²=AB²+BC²

Proof:-

In ΔABC, m∠B=90.

Let line-segment BD⊥AC

When an altitude is drawn to the hypotenuse of a right angled triangle, then each side of triangle other than the hypotenuse is the Geometric Mean of Hypotenuse and the segment of Hypotenuse adjacent to it.

∴AB²=AD*AC
and BC²=CD*AC

So, AB²+BC²= AD*AC + CD * AC
                     = AC (AD + CD)
                     = AC *AC
         AB²+BC² = AC²

Answer 2

here is your answer....