Question

prove that converse of Pythagoras theorem​

Answer 1

Explanation:

the Converse of Pythagoras Theorem states that in a right triangle if the square of one side is equal to the squares of other two sides then the angle opposite to the first side is the right angle

Answer 2

hi mate,

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.