Question

what is the converse of Pythagoras theorem??
If you don't know don't answer please....​

Answer 1

The converse of the Pythagorean Theorem is: If the square of the length of the longest side of a triangle is equal to the sum of the squares of the other two sides, then the triangle is a right triangle.

Answer 2

Converse of Pythagorean Theorem states that:

In a triangle, if the square of one side is equal to the sum of the squares of the other two sides then the angle opposite to the first side is a right angle.

For example:-

Given: A ∆PQR in which PR2 = PQ2 + QR2

To prove: ∠Q = 90°

Construction: Draw a ∆XYZ such that XY = PQ, YZ = QR and ∠Y = 90°

Converse of Pythagorean Theorem

{ Attached Figure }

So, by Pythagora’s theorem we get,

XZ2 = XY2 + YZ2

⇒ XZ2 = PQ2 + QR2 ……….. (i),

[since XY = PQ and YZ = QR]

But, PR2 = PQ2 + QR2 ………… (ii),

[given]

From (i) and (ii) we get,

PR2 = XZ2 ⇒ PR = XZ

Now, in ∆PQR and ∆XYZ,

we get,

PQ = XY,

QR = YZ and

PR = XZ

Therefore ∆PQR ≅ ∆XYZ

Hence ∠Q = ∠Y = 90°

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