Question

Show that if the diagonal of a quadrilateral bisect each other at right angles ,then it is rhombus​

Answer 1

Step-by-step explanation:

in triangle adc and dbc

congruent this triangle

then the areas of both triangle

are equal

then by the theorem 12.5 equal it's side so then it proof 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.