Question

Show that if the diagonals of a quadrilateral bisect each other at right angles , then is a rhombus .
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Answer 1

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 .

Answer 2

Step-by-step explanation:

Take quadrilateral ABCD , AC and BD are diagonals which intersect at O.

In △AOB and △AOD

DO=OB ∣ O is the midpoint

AO=AO ∣ Common side

∠AOB=∠AOD ∣ Right angle

So, △AOB≅△AOD

So, AB=AD

Similarly, AB=BC=CD=AD can be proved which means that ABCD is a rhombus.