Question

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


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Answer 1

Answer:

Step-by-step explanation:

The diagonals are AC and BD

Let the diagonals bisect each other at O.

In ΔAOBandΔAOD

OA=OA (common)

OB=OD (given the bisect)

∠AOB=∠AOD (each 90  

0

)

∴ΔAOB≅ΔAOD (SAS criteria)

The corresponding parts are equal.

AB=AD

Similarly, AB=BC

BC=CD

CD=AD

∴AB=BC=CD=DA

i.e. the quadrilateral is a Rhombus

solution