Question

State and prove : The converse of the
Pythagoras theorem.​

Answer 1

Answer:

naaku teliyadhu

Explanation:

naak teliyad

Answer 2

Answer:

Let us assume the Pythagoras theorem is already proved.

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

Converse of Pythagoras theorem

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

Converse of Pythagorean Theorem Proof

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.

Formula

As per the converse of the Pythagorean theorem, the formula for a right-angled triangle is given by:

a2+b2 = c2

Where a, b and c are the sides of a triangle.