Converse of the Pythagorean Theorem
The converse of the Pythagorean Theorem is a statement that is derived from the original theorem
The converse of the Pythagorean Theorem is a statement that is derived from the original theorem.
The original Pythagorean Theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. Mathematically, it can be expressed as:
a^2 + b^2 = c^2
Where ‘a’ and ‘b’ are the lengths of the two legs of the triangle, and ‘c’ is the length of the hypotenuse.
The converse of this 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 lengths of the other two sides, then the triangle is a right triangle.
So, to state it more formally:
If a triangle has side lengths ‘a’, ‘b’, and ‘c’, and if a^2 + b^2 = c^2, then the triangle is a right triangle.
In other words, if the equation holds true, it guarantees that the triangle is a right triangle. This is useful when we want to prove that a given triangle is a right triangle by using the converse of the Pythagorean Theorem.
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