How do you describe the properties of the diagonals of a parallelogram.
Opposite sides are congruent, opposite angles are congruent, and the consecutive angles are supplementary.
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If this is a true parallelogram, both sets of opposite sides and angles must be equal. If one set is not equal, the lines will not be parallel. If you extend the lines through the sides, you can see the similarity between the points of intersection, in terms of the angles. Use straws, sticks, or strings to experiment with the lengths of the sides, to give you something real to prove it to yourself.
I misread the question. I apologize.
Bill is right. If you draw lines through the parallelogram, from one corner to its opposite, then, connecting the other two opposite corners, you will create four triangles, as you do when playing with drawings of squares.
Similar to when you are able to cut a pie perfectly, you will end up with "slices" that are equal. However, in a parallelogram, two of your slices will be equal to each other, and the other two will be equal to each other, unless all four sides are equal in length, as in a square or rhombus where all of the "slices" will be the same.
Also, as Bill pointed out, the diagonal lines will be cut exactly in half by each other.
I like to draw these out on graph paper with a ruler, as well. Then, you can measure your lines, and see that your diagonals bisect each other.