Question

Proof Of Pythagoras Theorem​

Answer 1

Step-by-step explanation:

Step-by-step explanation:

Pythagoras' theorem :-

→ In a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.

Step-by-step explanation:

It's prove :-

➡ Given :-

→ A △ABC in which ∠ABC = 90° .

➡To prove :-

→ AC² = AB² + BC² .

➡ Construction :-

→ Draw BD ⊥ AC .

➡ Proof :-

In △ADB and △ABC , we have

∠A = ∠A ( common ) .

∠ADB = ∠ABC [ each equal to 90° ] .

∴ △ADB ∼ △ABC [ By AA-similarity ] .

⇒ AD/AB = AB/AC .

⇒ AB² = AD × AC ............(1) .

In △BDC and △ABC , we have

∠C = ∠C ( common ) .

∠BDC = ∠ABC [ each equal to 90° ] .

∴ △BDC ∼ △ABC [ By AA-similarity ] .

⇒ DC/BC = BC/AC .

⇒ BC² = DC × AC. ............(2) .

Add in equation (1) and (2) , we get

⇒ AB² + BC² = AD × AC + DC × AC .

⇒ AB² + BC² = AC( AD + DC ) .

⇒ AB² + BC² = AC × AC .

Hence, it is proved.

Answer 2

Introduction to Pythagoras Theorem:-

Pythagoras of Samos (570 B.C. – 495 B.C.) was a famous great mathematician and philosopher. Pythagoras’ Theorem was his most important contribution to the study of right angled triangles.

Hypotenuse:- The hypotenuse is the longest side of a right-angled triangle. It lies opposite the right angle. The other two sites are called the legs of the right triangle.

Result 1. In a right triangle, the hypotenuse is the longest side.

Proof In a right ∆ABC, we have

c² = a² + b² [by Pythagoras’ Theorem]

→ c² > a² and c² > b²

→ c > a and c > b.

Thus, in a right triangle, the hypotenuse is greater then each of the remaining two sides.

Hence, in a right triangle, the hypotenuse is the longest side.