Question

show that if the diagnols of a quadrilateral are equal and bisect each other at. right angle, then it is a quadrilateral

​

Answer 1

Answer:

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° )

∴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