Question

if the diagonals of a quadrilateral bisect each other, then the quadrilateral must be a parallelogram.
True or false?

Answer 1

Not necessarily.

Answer 2

True. You will have constructed 4 triangles and opposite triangles will be congruent by SAS. That will mean, using corresponding parts of congruent triangles opposite sides will be equal, and parallel.

Therefore, a parallelogram

Answer 3

Give me a minute and I can get you a graphic.

Answer 4

In the graphic, after we establish the top and bottom triangles are congruent, it follows the top and bottom sides are equal and m(angle 1)=m(angle2) and m(angle 3)=m(angle 4). Doing the same with the left and right triangles, we get that those side are also equal and the opposite angles of the quadrilateral are equal.

Answer 5

it is true thanks!!!!!

Answer 6

my pleasure