Answer:
Step-by-step explanation:
We have to prove that the diagonals of parallelogram bisect each other.
Consider, ABCD is a parallelogram with AC and BD as diagonals and M is the point of intersection of the two diagonals.
We have to prove that MA=MC and MB=MD.
Now, In ΔAMD and ΔBMC, we have
∠MAD=∠MCB (Alternate angles as ABCD is parallelogram and DC║AB)
AD=BC (Opposite sides of parallelogram)
∠ADM=∠MBC (Alternate angles as ABCD is parallelogram and DC║AB)
Thus, by SAS rule of congruency,
ΔAMD ≅ ΔBMC
⇒MA=MC and MB=MD (CPCT)
Therefore, we use the method of congruent triangles in order to prove that diagonals of parallelogram bisect each other.
Hence, option A is correct.