How to prove that diagonals of rhombus bisects its angles?
Given: ABCD is a Rhombus
⇒AB=BC=CD=AD
To Prove:
∠BAC=∠DAC
and
∠DCA=∠BCA
Proof:
In ΔADC and ΔABC
AB=AD [Given]
CD=CB [Given]
AC=AC [Common]
⇒ΔADCΔABC[By SSS congruence criterion]
∠BAC=∠DAC [By cpct]
∠DCA=∠BCA [By cpct]
Hence the result.