### What figure is formed? - December 1995

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What figure is formed when the consecutive midpoints of the sides of a quadrilateral are joined? What if the original quadrilateral were a rectangle? A kite? An isosceles trapezoid? A square? A rhombus? Other shapes? Explain why you think your answer is true.

Annie says:

Another excellent group of solutions! We received 53 solutions for December. All but six got the general answer. Of those six, most said "The figure you get is a quadrilateral," but while that is technically a true statement, I wanted something more specific, like "parallelogram."

I was looking for four main things when rating the solutions, and sort of in order of importance. First, did you get the general case correct? Second, did you prove the general case? Third, did you provide examples? Fourth, did you prove the examples? I was also looking for solutions that were well thought-out and organized.

Probably over half of the submissions have the general form right and got the proof of it as well. Twenty-two people scored a "2"; most of them got those two important parts. Four teams got a "3", which I will talk about in a bit, and four teams scored a "4", sort of. For some ideas about how the winners were chosen, read the comments included with their entries.

Again, there were a lot of "right" answers submitted that didn't win. It is hard to have to choose, but there are always a few solutions that are not only right, but are better, or more complete, than the other solutions. If you would like feedback on your solution, just drop me a note. After I figure out how to clone myself, I will write back to everyone personally!

I like this problem. We used it once before, a long time ago, but we didn't get any answers nearly as good as the ones we got this time!

Here are the honorees this month. We have one winner, three honorable mentions, and one special mention.

### December Project of the Month

#### Special Mention

The winners receive certificates and totally cool Geometry Forum t-shirts which say on the back "Winners, Project of the Month, 1995-96." Honorable mention recipients get certificates and some pretty cool keychains. Well worth the effort in either case.

- Annie