Inscribed and Circumscribed circles with Patty Paper Geometry

We tried another project from Patty Paper geometry today for our Family Math project. I can’t say enough good things about this book – studying geometry through folding is absolutely incredible.

Here’s the book:

Patty Paper Book

There were two parts to our project today – studying a bit about the circumscribed circle and then the inscribed circle. We started off the first part by talking about perpendicular bisectors:

 

In the second part of our discussion about perpendicular bisectors we tried to understand why the perpendicular bisectors met at a point that was the same distance from each vertex. It took a couple of minutes for the kids to get the idea, but it was a great discussion:

 

We wrapped up the discussion of perpendicular bisectors by drawing the circumcircle of our triangle and talking about (but not proving) a neat area formula:

 

For the second part of the project we discussed angle bisectors and the inscribed circle of a triangle. We also switched to a darker pen so that our lines showed up better 🙂

Part 1 of this section involved drawing a triangle and using folding to make the angle bisectors:

 

Next we discussed why the angle bisectors in a triangle intersected at a point that was equally distant from all three sides (this part of the project involves a really clever use of the patty paper):

 

Finally, we wrapped up the project by discussing the inscribed circle and one property of the inscribed circle that my son noticed. The second part was a little tough, but we got through it and the boys understood a new area formula for a triangle:

Area = (1/2) * (radius of the inscribed circle)*(Perimeter)

Fun!

 

Again, I can’t saw enough good things about this geometry book. It is amazing to watch kids play around with ideas from geometry by folding paper. The two topics from today are pretty advanced, but are easily accessible to kids – and fun – through the approach Patty Paper Geometry takes!

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