Squares that aren't squares?

Updated with solutions!

Today I want to highlight a square problem I saw at MathNotations. I hope Dave Marain doesn't mind me showing this picture and problem on my blog... I have no problem acknowledging it's from his blog. I COULD just tell you all to "go read it at Dave's blog....

BUT I don't feel that's the best way, IF I want you to think about this. I can just guess that most of the folks would feel too lazy to click on the link and go read it there (would you?). So I want to show it here.

Figures not drawn to scale! And this is important!

Now here's the question:
Does the given information in each diagram guarantee that each is a square?

If you don't think so, your mission is to draw a quadrilateral with the given information but that clearly does NOT look like a square.

The IDEA is to make our students THINK LOGICALLY, or practice their deductive reasoning skills. A great little problem.

The answers:

Figure 1 is not necessarily a square. The upper left corner angle can be of any size. The upper side can be of any length. And so on. See here two examples.

Figure two is not necessarily a square either since the "top" side can be of any length. But it is a rectangle.

Figure 3 in the original problem IS always a square!

Now, I'll write another post where we'll extend this idea to some parallelograms.


Dave Marain said…
Thank you for the support and the link, Maria!

We're both committed to balancing strong skills development with critical thinking. Teaching children to reason requires that we provide experiences and challenges outside of the prescribed curriculum. There are many wonderful sources of such problems out there on the Web. You and Denise are to be commended for helping parents find them.

Dave Marain

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