Question

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

Answer 1

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.

Answer 2

Answer

The concept can be used to prove that the diagonals of a parallelogram bisect each other is congruent triangles

Explanation

In a parallelogram, opposite sides are equal and parallel.

The two diagonals in the parallelogram make four triangles. opposite triangles are congruent. That means two pair of congruent triangle are here.

Using congruence of triangles, we can prove the diagonals of a parallelogram bisect each other