Dear Math for Mom & Dad,

My child likes to make things out of paper, tape, and cardboard. How can I use that interest to foster her interest in geometry?

Geometry Mom

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Dear Geometry Mom,

Use this activity to find an interior point of a cardboard triangle on which the entire triangle will balance.

Begin by finding the midpoint of each side of an acute triangle. If you have a paper template of the triangle, you could fold each side of the triangle on itself, endpoint to endpoint, then identify the midpoint by creasing the paper. When the paper template is placed on top of the cardboard triangle, use the creases to mark the midpoint of each side. Alternatively, you could measure the length of each side of the cardboard triangle, divide by 2, then find the midpoints by measurement. Better yet, do it both ways and discuss the merits and limitations of each approach.

Next, draw segments called

*medians* from each vertex to the midpoint of the opposite side. As seen in the figure below, the medians of a triangle intersect at a point called the

*centroid*. This point is also called the

*center of gravity* of the triangle, the point where a cut-out version of the triangle will balance on the point of a pen or pencil.

Try this same approach with a right triangle. With an obtuse triangle. Does it always work?

To find the centroid of a quadrilateral, connect the midpoints of opposite sides. These

*bimedians *intersect at the centroid. Try this with several quadrilaterals. Does it always work?

For additional resources and ideas, visit my website math-ed.com

Copyright David A. Thomas 2010 All Rights Reserved