Question

write converse of phthagorus theorum and prove it​

Answer 1

Theorem:

The converse of Pythagoras theorem states that “If the square of a side is equal to the sum of the square of the other two sides, then triangle must be right angle triangle”.

Proof of Converse of Pythagoras theorem:

Statement: If the length of a triangle is a, b and c and c² = a² + b², then the triangle is a right-angle triangle.

[ Refer to the first attachment ]

Proof: Construct another triangle, △EGF, such as AC = EG = b and BC = FG = a.

[ Refer to the second attachment ]

In △EGF, by Pythagoras Theorem:

⇒EF² = EG² + FG2² = b² + a² …………(1)

In △ABC, by Pythagoras Theorem:

⇒AB² = AC² + BC² = b² + a² …………(2)

From equation (1) and (2), we have;

⇒EF² = AB²

⇒EF = AB

⇒ △ ACB ≅ △EGF (By SSS postulate)

⇒ ∠G is right angle

Thus, △EGF is a right triangle.

Hence, we can say that the converse of Pythagorean theorem also holds.

Hence Proved!!