Any theorem is derived by using basics of that topic, properties of the object / structure the proof is being worked upon.
To start with a proof, recall the properties of the structure. For example, in this case (prove that diagonals of a rhombus are perpendicular bisectors of each others) recall the properties of a rhombus.
- a parallalogram (opposite sides are parallel to each other).
- All sides are equal.
First we will prove that the diagonals are bisectors of each other.
△ BEA is congruent to △ DEC by AAS rule. (I am just mentioning the short steps, in an examination you will have to write down all the intermediate steps too).
As the triangles are congruent like this, thus DE = BE and AE = EC --> E is the mid point of both diagonals, thereby proving that in rhombus, the diagonals bisect each other.
Then we will prove that the diagonals are perpendicular to each other.
△ BAE is congruent to △ BCE by SSS rule (BA=BC as in rhombus all sides are equal, AE=EC as we have proved above that diagonals have bisected each other, BE=BE).
Now therefore ∠BEA = ∠ BEC
and we also know ∠BEA + ∠ BEC = 180
Therefore ∠BEA = ∠ BEC = 90°.
I would suggest you refer to NCERT Math textbook to see precise steps that should be elaborated in board exam.