Which concept can be used to prove that the diagonals of a parallelogram bisect each other?
congruent triangles
similar triangles
congruent rectangles
similar rectangles

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.

so option A is correct.

Congruent triangles

Explanation:

Because the definition of congruent triangles: The angles have the same line lengths and the same angle measures.

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