Question

in a quadrilateral if the diagonals bisect each other then prove that this quadrilateral is a parallelogram

Answer 1

Yes , you can prove this by…

Answer 2

THEOREM: If a quadrilateral is a parallelogram, it has 2 sets of opposite angles congruent. ... THEOREM: If a quadrilateral has diagonals which bisect each other, then it is a parallelogram. * THEOREM: If a quadrilateral has one set of opposite sides which are both congruent and parallel, then it is a parallelogram.

Given: AM = MC, DM =MB

First, do you see the vertical angles in the middle? They’re congruent.

That, with the congruent segments proves two pairs of congruent triangles with SAS.

If these triangles are congruent, then the rest of the corresponding angles must be congruent.

It looks like we have congruent alternate interior angles now, so the transversal lines must be parallel.

Since both pairs of opposite sides are parallel, we have a parallelogram.