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Solution:
Given: ABCD is a Rhombus
To Prove: ΔABC≅ΔCDA
Construction: Join AC as diagonal.
Proof: ABCD is Rhombus whose sides are equal and diagonal are perpendicular bisectors. Please see attach figure.
In ΔABC and ΔCDA
AB=CD (Side of same Rhombus)
BC=DA (Side of same Rhombus)
AC=CA (Common Side of both triangle)
Therefore, ΔABC≅ΔCDA by SSS property of congruence.
Hence Proved, ΔABC≅ΔCDA
