Geometry Challenge for January 23

Today was one of those days when I decided to totally change my plan for math and it worked out tremendously better than the original plans. Let me tell you about it. 🙂

My kids are used to what I call “geometry challenges”, where they have to prove that a statement is true, by using what they know as mathematicians.  The first one we did was to prove that the shortest distance between two points is a straight line.  They worked alone or with a partner to show how that was true, or to find a way to prove that it wasn’t.  Then next one was to prove that a straight angle equals 180 degrees.  With that one, they used Power Polygons with angles that they know to show whether that statement was true or untrue.  Needless to say, they’ve totally rocked each of those situations, and really shown what they know about geometry.

So today I was headed in a totally different direction, but decided to do today’s lesson as a challenge again.  Here is what they were asked to do:

Like in the past, they had amazing things to show for the work on this challenge.  Before I show you what they did, I’m curious to know what your answer would be.  Could you answer this challenge?

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