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Describe the properties of the diagonals of a parallelogram.

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2 Answers

Opposite sides are congruent, opposite angles are congruent, and the consecutive angles are supplementary.

Read if you need more detail:

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.

Edit:

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.

Adding more information about the diagonals in a Parallelogram:

In a parallelogram, diagonally-opposite angles are equal.  Diagonals drawn which divide these agles into two angles in each corner create opposite equal angles:  the inside corner angles made between a diagonal and any one side = the angles made at the other end of the diagonal and the opposing equivalent side.

Diagonals create triangles:  twice as many triangles as there are diagonals.  These triangles are congruent (equal in all 3 sides and 3 angles) if one of them is flipped or inverted and compared with the triangle directly opposite it.

Two diagonals bisect each other: a crossing diagonal divides the diagonal it crosses exactly in half.

 

Comments

I'm glad you responded! I misread the question.