Question

show that if the diagonals of a quadrilateral bisect each other at right angle then it is a rhombus ​

Answer 1

you can easily prove this by congruency

Step-by-step explanation:

first congruent opposite triangles so as to make opposite sides equal then congruent adjacent triangles so as to make adjacent sides equa

Answer 2

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