Question

State and prove converse of Pythagoras theorem.​

Answer 1

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Answer 2

hi mate,

Converse of Pythagoras theorem is defined as: “If square of a side is equal to the sum of square of the other two sides then triangle must be right angle triangle”.

Whereas Pythagorean theorem states that the sum of the square of two sides (legs) is equal to square of the hypotenuse of a right-angle triangle.

But, in the reverse of the Pythagorean theorem, it is said that if this relation satisfies, then triangle must be right angle triangle. So, if the sides of a triangle have length, a, b and c and satisfy given condition a2 + b2 = c2, then the triangle is a right-angle triangle.

Proof:

Construct another triangle, △EGF,

such as AC = EG = b and BC = FG = a.

In △EGF, by Pythagoras Theorem:

EF²= EG2 + FG² = 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.

i hope it helps you