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.

Alpha6 said:

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.

Click to expand...

Have you ever seen an isosceles trapezoid?

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

Alpha6 said:

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.

Click to expand...

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.

Dr.Peterson said:

Have you ever seen an isosceles trapezoid?

Click to expand...

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.

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

Alpha6 said:

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.

Click to expand...

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.