Mathematics for Teaching Embedding the idea of functions in geometry lessons

## Embedding the idea of functions in geometry lessons

GeoGebra is a great tool to promote a way of thinking and reasoning about shapes. It provides an environment where students can observe and describe the relationships within and among geometric shapes, analyze what changes and what stays the same when shapes are transformed, and make generalizations.

When shapes or objects are transformed or moved, their properties such as location, length, angles, perimeters, and area changes. These properties are quantifiable and may vary with each other. It is therefore possible to design a lesson with GeoGebra which can be used to teach geometry concepts and the concepts of variables and functions. Noticing varying quantities is a pre-requisite skill towards understanding function and using it to model real life situations. Noticing varying quantities is as important as pattern recognition. Below is an example of such activity. I created this worksheet to model the movement of the structure of a collapsible chair which I describe in this Collapsible chair model.

Show angle CFB then move C. Express angle CFB in terms of δ, the measure of FCB. Show the next angle EFB then move C. Express EFB in terms of δ. Do the same for angle FBG.
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Because CFB depends on FCB, the measure of CFB is a function of δ. That is f(δ) = 180-2δ. Note that the triangle formed is isosceles. Likewise, the measure of angle EFB is a function of δ. We can write this as g(δ) = 2δ. Let h be the function that defines the relationship between FCB and FBG. So, h(δ)=180-δ. Of course you would want the students to graph the function. Don’t forget to talk about domain and range. You may also ask students to find a function that relates f and g.

For the geometry use of this worksheet, read the post Problems about Perpendicular Segments. Note that you can also use this to help the students learn about exterior angle theorem.
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