How To Determine If A Triangle Is Right

The Converse of the Pythagorean Theorem We assume that you are familiar with the Pythagorean Theorem. The opposite of the Pythagorean Theorem is: Read: how to determine if a triangle is correct 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 I.e. in ΔABC, if c 2 = a 2 + b 2 then ∠C is a right triangle, ΔPQR is a right angle.Read more: how long does it take to backup iphone | Top Q&AWe can prove this by contradiction. Assume that c 2 = a 2 + b 2 in ΔABC and that the triangle is not a right triangle. Now consider another triangle ΔPQR. We construct ΔPQR such that PR = a, QR = b and ∠R are right angles. According to the Pythagorean Theorem, (PQ) 2 = a 2 + b 2. But we know that a 2 + b 2 = c 2 and a 2 + b 2 = c 2 and c = AB. Read more: How to fold a treadmill according to the Nordic track So, (PQ) 2 = a 2 + b 2 = (AB) 2. That is (PQ) 2 = (AB) 2. Because PQ and AB are degrees length of the sides so we can take a positive square root. PQ = AB That is, all three sides of ΔPQR are congruent to the three sides of ΔABC. Therefore, the two triangles are congruent by the Side Congruence Property. Since ΔABC is congruent to ΔPQR and ΔPQR is a right triangle, ΔABC must also be a right triangle. Read more: Zong Balanced Share Code | How to transfer | Top Q&A This is a contradiction. Therefore, our assumption must be wrong.

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