Question

state and prove pythagoras theroem? ​

Answer 1

EXPLANATION.

Pythagoras theorem.

As we know that,

In a right angled triangle the square of the hypotenuse is equal to the other two sides.

⇒ ΔABC Right angled at B.

⇒ ΔADB ≈ ΔABC.

By using property [similar triangle of same ratio], we get.

⇒ AD/AB = AB/AC.

⇒ AD.AC = AB² ⇒ (1).

⇒ ΔBDC ≈ ΔABC.

⇒ CD/BC = BC/AC.

⇒ CD.AC = BC² ⇒(2).

From equation (1) & (2), we get.

Add both the equations (1) & (2), we get.

⇒ AB² + BC² = AD.AC + CD.AC.

⇒ AB² + BC² = AC(AD + CD).

⇒ AB² + BC² = AC(AC).

⇒ AB² + BC² = AC².

HENCE PROVED.