Our next unit was on Similarity. My original plan for the curriculum is to have a unit on similarity and then a unit on right triangles. Since I am not teaching Common Core Geometry this year, I combined the two units into one and only taught the aspects of right triangles that need to be covered (ie: no Trigonometry). That is pretty much how I taught it last year anyway. This year I taught things in a different order, but as I was teaching it, I was unhappy with the order I came up with. It was too late to fix it though and so we plugged on.
I started with the Pythagorean Theorem. This felt a little funny because we have been using the Pythagorean Theorem all year. What was new for the students was Pythagorean Triples (which students are just now finally starting to remember) and the Converse of the Pythagorean Theorem.
Next we did the Triangle Proportionality Theorem. Last year I taught two other proportionality theorems along with this one. I'm wondering if I'll have to add them back in for next year. Anyway, I took them out so my students could focus on the main theorem. I introduced them to the other two theorems later during a practice activity.
Then we did the Mean Proportional. I really struggled to teach this last year. It was the first time I'd ever seen this, and I understood it, but I could not for the life of me explain it well enough to my students. This year I jumped right into a formula for calculating the Mean Proportional. My students were much better able to answer questions about the Mean Proportional this year. After teaching the formula method, I intended to go back and reteach it explaining the three similar triangles. (Note: we did not even cover similarity yet in this unit; I wanted to get all of the right triangle topics covered first.) I never was able to go back to this topic, but we do have a ton of review coming up.
I began the true similarity portion of this unit with Dilations as Common Core suggests. Students loved these, but some mistakenly added the scale factor instead of multiplying it. The next day we studied Dilations with Compositions. I liked having this separate from the congruence transformations because allowed for review.
Next we covered Similar Polygons and verifying that polygons are similar.
Then we used similar polygons to solve for missing lengths.
Following that, we went over Similarity Proof. On the first day, I introduced them to the three Postulates/Theorems that prove figures are similar. For this lesson, there were so many diagrams and so much writing that I made two sheets of handouts and fill in the blank notes for students to glue into their notebooks.
The next day we did formal twocolumn proofs using the Angle Angle Similarity Postulate. For this we did a worksheet and stapled it into our notebooks.
After more practice, we concluded our similarity unit. Sadly I did not come up with any interesting or "fun" ideas to use in our notebooks. I'm starting to brainstorm what I can do differently for next year already.
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