Is it true that if ΔABC is a right-angled triangle and the length of the hypotenuse is b and other two sides are of length a, c then $b 2 = a 2 + c 2$ . The converse of this statement will be if the lengths of triangles a, b, c are related as $b 2 = a 2 + c 2$ Then the triangle is right-angled?

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Detailed Solution

We know that in a right-angled triangle there is one right angle of measure 90̊̊̊ and side opposite to it called the hypotenuse. The Pythagoras theorem states that in a right-angled triangle the square of the length of the hypotenuse is the sum of squares of lengths of other two sides”.
We see in the statement of the Pythagoras theorem that the premise or assumption is that the triangle is right-angled and the conclusion is that the square of the length of the hypotenuse is the sum of squares of lengths of the other two sides.
In order to converse, we take the conclusion of the Pythagoras theorem as the premise and the premise as the conclusion. We have a triangle and we do not know which one is the hypotenuse. So the converse statement will be “If the sum of squares of lengths of two sides in a triangle is equal to the square of the third side, then the triangle is right-angled.”
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In symbols by Pythagoras theorem,
if ΔABC is a right-angled triangle and the length of the hypotenuse is b and other two sides are of length a, c then