Your assignment this weekend:

Don't lose your worksheet from Wednesday, I'll want to collect it Monday.

Task 1: In class we/you discovered that if you start with a pair of chords BC and DE in a circle that intersect at a point F, and you add a pair of opposite segments to make two triangles, then those triangles are similar.

Then, by using the fact that they are similar, we wrote down a proportion of corresponding sides, and cross multiplied the proportion to get that (DF)(FE) = (CF)(FB).

Your task is to write down the details of the reasoning we used to prove that the triangles are similar, and then to deduce the equation above. I'm not expecting any specific form to your explanation--this is a formative assessment for me to see what your preferred way of explaining things is. I do expect to get words on paper from you.

Task 2: Download Geogebra--it's cool, you're going to want it. I suggest using one of the offline installers (they seem to work better for me).

Task 3 (an exploration): On Geogebra, or on a sheet of paper, make the following diagrams:

The size of the angle at E and I doesn't matter, but the rays of the angle should each intersect the circle twice.

a. In the diagram on the left, I have drawn in some central angles that intercept the same arcs as the angle at I. Look for a relationship between those three angles. Try to write an equation to show that relationship that says: the measure of the angle at I is equal to ...

b. In the diagram on the right, there are rather a lot of triangles. Here are a few of them: ΔEFG, ΔEHG, ΔEFB, ΔEHB, ΔEFG, and a bunch more that use M. Now, we already figured out the triangles that include M as a vertex that are similar, but I'm pretty sure there is also at least one pair of triangles that include E as a vertex that are similar. Find the pair of similar triangles.

Task 4: look at the list of topics. Keeping in mind that

• a lot of these topics will spread over multiple days, and you will only be responsible for one day
• I will provide you with some resources to work from (you won't be responsible for figuring it all out on your own)

Think about which topics you would prefer to teach. Ideally you would pick a topic you know something about, and would be interested in learning more.