Midpoints of a quadrilateral

I was looking at a blog polymathematics and I saw a reference to a nice geometry fact.

If you join the midpoints of a quadrilateral it is always a parallelogram.

When I first saw this result, back in high school, I was totally amazed (couldn't quite believe) specially for weird quadrilaterals.... so I draw a nice big weird quadrilateral in the back of my book, joined the midpoints and saw it!! (I still have the book)

If you don't want spoils don't read below.



The key is to draw the diagonals...

Well, you can find a demonstration here at "Cut the knot" as usual with a nice java application so you can convince yourself.

Just some nice memories...

1 comment:

Unknown said...

So... Math in english is most weird for me than in portuguese! OMG! hehehe But.. nice! just for remember me how much smart you are.. I really dont know what you're talking about, baby... shamee!! one day, you'll show me that notebook, wonder see it!
is everything in english, so I write in english too...
I like colors, but is just my opinion... do in your own way your blog! soooo I'll stop to bored you here... but... it's because, I miss you!!!

kisses..
Carol