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If we consider two triangles ΔABC and ΔPQR where c 2 = a 2 + b 2 then we can say ∠C is a right triangle. The converse of the Pythagoras theorem states that 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. How Do You Prove the Converse of Pythagoras Theorem? The converse of Pythagoras theorem formula is c 2 = a 2 + b 2, where a, b, and c are the sides of the triangle. What is the Formula for Converse of Pythagoras Theorem? The coverse of the Pythagoras 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 the first side is a right angle. In other words, we can say, in a right triangle, (Opposite) 2 + (Adjacent) 2 = (Hypotenuse) 2.įAQs on Converse of Pythagoras Theorem What is the Converse of Pythagoras Theorem? Here, AB is the base, AC is the altitude or the height, and BC is the hypotenuse. In the given triangle ABC, we have BC 2 = AB 2 + AC 2. The Pythagoras theorem states that if a triangle is right-angled (90 degrees), then the square of the hypotenuse is equal to the sum of the squares of the other two sides. If the sum of the squares of two sides of a triangle is greater than the square of the hypotenuse, the triangle is an acute triangle. If the sum of the squares of two sides of a triangle is less than the square of the hypotenuse, the triangle is an obtuse triangle.ģ. If the sum of the squares of two sides of a triangle is considered equivalent to the square of the hypotenuse, the triangle is a right triangle.Ģ.
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Once the triangle is identified, constructing that triangle becomes simple. The main application of the converse of the Pythagorean theorem is that the measurements help in determining the type of triangle - right, acute, or obtuse. The converse is the complete reverse of the Pythagoras theorem.
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The converse of Pythagoras theorem states that 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. What is the Converse of Pythagoras Theorem?