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Step-by-step explanation:

We can prove this by contradiction.

Let us assume that c2=a2+b2 in ΔABC and the triangle is not a right triangle.

Now consider another triangle ΔPQR. We construct ΔPQR so that PR=a, QR=b and ∠R is a right angle.

By the Pythagorean Theorem, (PQ)2=a2+b2.

But we know that a2+b2=c2 and a2+b2=c2 and c=AB.

So, (PQ)2=a2+b2=(AB)2.

That is, (PQ)2=(AB)2.

Since PQ and AB are lengths of sides, we can take positive square roots.

PQ=AB

That is, all the three sides of ΔPQR are congruent to the three sides of ΔABC. So, the two triangles are congruent by the Side-Side-Side Congruence Property.

Since ΔABC is congruent to ΔPQR and ΔPQR is a right triangle, ΔABC must also be a right triangle.

This is a contradiction. Therefore, our assumption must be wrong.

Step-by-step explanation:

We can prove this by contradiction.

Let us assume that c2=a2+b2 in ΔABC and the triangle is not a right triangle.

Now consider another triangle ΔPQR. We construct ΔPQR so that PR=a, QR=b and ∠R is a right angle.

By the Pythagorean Theorem, (PQ)2=a2+b2.

But we know that a2+b2=c2 and a2+b2=c2 and c=AB.

So, (PQ)2=a2+b2=(AB)2.

That is, (PQ)2=(AB)2.

Since PQ and AB are lengths of sides, we can take positive square roots.

PQ=AB

That is, all the three sides of ΔPQR are congruent to the three sides of ΔABC. So, the two triangles are congruent by the Side-Side-Side Congruence Property.

Since ΔABC is congruent to ΔPQR and ΔPQR is a right triangle, ΔABC must also be a right triangle.

This is a contradiction. Therefore, our assumption must be wrong

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