1. ## Help (proving quadrilateral is a parallelogram).

I said "yes" but got it wrong. An explanation someone told me was that we do not know for sure that the 2 legs are parallel or that the top and bottom are congruent.

However, this confuses me. If the legs are the same length but not parallel how could the tops be parallel?

I tried it with 4 pencils and it does not work.

2. Originally Posted by Alpha6
I said "yes" but got it wrong. An explanation someone told me was that we do not know for sure that the 2 legs are parallel or that the top and bottom are congruent.

However, this confuses me. If the legs are the same length but not parallel how could the tops be parallel?

I tried it with 4 pencils and it does not work.

Have you ever seen an isosceles trapezoid?

3. ## If the two horizontal lines are parallel, it is a parallelogram.

Originally Posted by Alpha6
I said "yes" but got it wrong. An explanation someone told me was that we do not know for sure that the 2 legs are parallel or that the top and bottom are congruent.

However, this confuses me. If the legs are the same length but not parallel how could the tops be parallel?

I tried it with 4 pencils and it does not work.

If you draw two vertical lines at the corners, the two line segments have equal length. Therefore, the two triangles formed by the two vertical lines are congruent. Then you can prove the two sides are parallel.

4. Originally Posted by Dr.Peterson
Have you ever seen an isosceles trapezoid?

Yes, I know in an isosceles trapezoid the 2 legs can be congruent and not parallel

but the isosceles trapezoid looks like this:

With the 2 legs facing in toward each other. The figure in the question looks nothing like that, which is why I'm confused.

5. ## when two opposite corners are both acute, it must be parallelogram.

Originally Posted by Alpha6
Yes, I know in an isosceles trapezoid the 2 legs can be congruent and not parallel

but the isosceles trapezoid looks like this:

With the 2 legs facing in toward each other. The figure in the question looks nothing like that, which is why I'm confused.
This problem should be in words, not in a picture like that. If you need a proof, let me know and I'll write one for you.

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