4. If the diagonals of a quadrilateral bisect each other at right angles, then which type of a
quadrilateral is it?
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Answer:
rhombus
Step-by-step explanation:
rhombus
Show that if the diagonals of a quadrilateral bisect each other at right angles, then it is a rhombus. Sol: We have a quadrilateral ABCD such that the diagonals AC and BD bisect each other at right angles at O. Their corresponding parts are equal. Thus, the quadrilateral ABCD is a rhombus.
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If two adjacent sides of a parallelogram are equal, then it is a rhombus. This test is often taken as the definition of a rhombus. A quadrilateral whose diagonals bisect each other at right angles is a rhombus.