The given statement is true or false:A quadrilateral is a rhombus if its diagonals cut each other at right angles.

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The given statement is false.Concept- Assume that a quadrilateral ABCD has two diagonals that are.Circles apart. Knowing that a rhombus has the property that all of its sides are equal, we may demonstrate that the quadrilateral is a rhombus by demonstrating that all of its sides are equal.A quadrilateral ABCD with its diagonals intersecting at point O is seen in the diagram below.Let us assume the length of diagonals A C as "  " and $B D$ as "  " in the above diagram.Now, as diagonals bisect each other so:We will now calculate the sides' lengths of the ABCD quadrilateral.The quadrilateral is divided into four right-angled triangles by the diagonals, allowing the right triangles to apply Pythagoras' theorem.Pythagoras' Theorem statesIn , applying Pythagoras theorem we get,Substituting  as  and  as  in the above equation we get,Using the square roots of both sides,Applying Pythagoras theorem in  we get,Substituting AO as  and  as  we get,Using the square roots of both sides,Applying Pythagoras theorem in  we get,Substituting O C as  and  as  we get,Using the square roots of both sides,Applying Pythagoras theorem in  we get,Substituting  as  and  as  we get,Using the square roots of both sides,You can see from the calculations above that all of sides A, B, C, D, and A D are equal in length, i.e.Since we have shown that all sides are equal, the rhombus's property that all sides are equal is satisfied.As a result, we have demonstrated that a quadrilateral is a rhombus when its diagonals intersect one another at right angles.Hence, the given statement is false.

The given statement is true or false:

A quadrilateral is a rhombus if its diagonals cut each other at right angles.

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