Out & About: Tricky Triangles

It all started with a lovely morning walk to the hardware store.  We needed a long tape measure for our 'measure the house' project that's been brewing for a while.

"Look, Mama!  A triangle!  Except...I didn't know triangles could do that.  I knew that two triangles make a square..."

And therein lies the rub, doesn't it? For a kid who has played with tangrams (right triangles) and pattern blocks (equilateral triangles) for years, those are what triangles 'are' aren't they?  Already shaped and scaled to make a whole of some other shape (rhombi, squares, rectangles, hexagons).  But there this triangle was, obviously not dividing the space evenly, just a modest, unbalanced slice out of this square-ish rectangle portion of the sidewalk.

As we walked further I wondered about how to respond to her observation.  As luck would have it, I had a stray piece of sidewalk chalk in my bag!

"There are a lot of ways to divide a square or rectangle into triangles.  Let's see how many we can find!"

A little later on, "Look!  More triangles!"

And here, a triangle?  She thought it was at first, but what does a triangle need to have to be a triangle?

Our eyes were open at that point, and we found other triangles on our journey.  Here are two with a square -- an almost- trapezoid in the wild!  (I say almost because of the curved bottom edge -- yes, there are shapes all around us but some of them are truly geometric and the others are not really geometric, like the 'triangular' yield sign with it's curved corners, and still others are 'natural' shapes which have their own wonderful rules.)

As a bonus, at the hardware store we found a section that specializes in tools used in real-life geometry -- things that help builders measure lengths, widths, diameters and angles! 

In closing, and in honor of triangles, take a look at this triangle interactive from the Triangulation Blog.  All you need to do is move your cursor/mouse.  I swear, it'll be worth your time.   Who knew triangles could be so funny!?

You may also be interested in a previous post, Channeling Tana Hoban: Juxtaposition Edition, where we discovered many, many more shapes on a similar walk, especially an incredible number of circles in juxtaposition with other shapes.