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

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

A diagonal is a line that divides a quadrilateral into two equal parts. This gives us two triangles. We know that a parallelogram is a quadrilateral because it has four sides.

If we make a diagonal in a parallelogram, we now have two congruent triangles. we can now use the concept of congruent triangles to show that the diagonals of a parallelogram bisect each other.

Learn more about a parallelogram: https://brainly.com/question/1563728