Given that abcd is a parallelogram, what must be proven to prove that the diagonals bisect each other?

We have to prove  Δ ABO ≅ Δ CDO or,  Δ DAO ≅ Δ BCO.

Step-by-step explanation:

Let us assume that ABCD is a parallelogram having diagonals AC and BD.

We have to prove that in a parallelogram the diagonals bisect each other.

Assume that the diagonals of ABCD i.e. AC and BD intersect at point O.

Therefore, to prove that the diagonals AC and BD bisect each other, we have to first prove that Δ ABO and Δ CDO are congruent or Δ DAO and Δ  BCO are congruent.

In symbol, we have to prove  Δ ABO ≅ Δ CDO or,  Δ DAO ≅ Δ BCO. (Answer)

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step-by-step explanation: