Question

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Converse Of ---Pythagorus Theorem---
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Answer 1

Hello buddy..... ✌

Answer:

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.

• That is, in ΔABC, if c2=a2+b2 then ∠C is a right triangle, ΔPQR being the right angle.

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.

HOPE IT WILL HELP YOU......

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Answer 2

Answer:

We assume you're familiar with the Pythagorean Theorem. 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