SOLUTION: how do you prove that a parallelogram is a parallelogram

Question 180217: how do you prove that a parallelogram is a parallelogram
Found 2 solutions by Mathtut, solver91311:
Answer by Mathtut(3670) (Show Source): You can put this solution on YOUR website!
what are the givens: obviously if your given that its a parallelogram then that is proof in itself that its a parallelogram. So, what is our givens????? thanks Mathtut
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

You don't have to prove that a parallelogram is a parallelogram. It just is. I know that is sort of a smart-a** answer, but you have really asked the wrong question. I'm reasonably certain that you want to know how to prove that a given quadrilateral is a parallelogram.

Going on that assumption, let's look at the definition of a parallelogram:

In geometry, a parallelogram is a quadrilateral with two sets of parallel sides. The opposite or facing sides of a parallelogram are of equal length, and the opposite angles of a parallelogram are of equal size.

So, you need to prove one of the following:

1. Each set of opposite sides are parallel

2. Each set of opposite sides are of equal length

3. Each set of opposite angles are of equal measure

Not knowing anything more than you told me about the characteristics of the quadrilateral in question, I can't tell you much more than this.

John

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