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.

thurgood marshall

explanation: in 1954, thurgood marshall and a team of naacp attorneys won brown v. board of education of topeka, kansas. in this landmark decision, the supreme court held that segregation in public education violated the equal protection clause of the fourteenth amendment.