The last two are opposite sides parallel and congruent theorem,
parallelogram diagonals converse

Explanation:

The parallelogram diagonals theorem says that if you have a parallelogram, then the diagonals bisect each other. This means the diagonals cut each other in half. Furthermore, it also means the two diagonals meet at the midpoint of each diagonal.

The converse takes this in reverse. If we know the two diagonals cut each other in half, then this must mean we are dealing with a parallelogram.

We can prove this by showing that triangle EHF is congruent to triangle GHD, where H is the intersection of the two diagonals. We use SAS in this case. From there, we then can see that the corresponding pieces of the two triangles are congruent. This leads to the alternate interior angles being congruent. The last piece of the puzzle is the alternate interior angles theorem converse, which shows the opposite sides EF and DG are parallel. A similar proof occurs to show that ED is parallel to FG.

the correct is answer is a 9-sided polygon!

t hope this

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