Upon finishing our quadrilaterals unit, we complete our congruence units. Then, we move on to Similarity. Similarity is a little mindset shift for students. In this unit, we move away from our simple equations, and start to set up proportions instead. Check out the pages we add to our geometry interactive notebook for our similarity unit.
Dilations Interactive Notebook Page
Many Geometry teachers like to teach dilations with the other transformations. Instead, I love to begin my Similarity unit with dilations. We start by defining dilation, scale factor, and center of dilation. Then, we make the important distinction that dilated figures are not congruent, but are similar instead. We discuss the properties of dilated figures, and then practice with performing dilations centered at the origin in the coordinate plane.
Dilations NOT Centered at the Origin
Dilations that are not centered at the origin is a newer topic in our curriculum, so I keep this lesson simple. We start by going over the steps, and then practice performing dilations. There are only 3 examples on our geometry interactive notebook page, so we also practice dilations using a dilations practice worksheet after we complete the notes.
Similar Polygons
Now that students have experienced similarity through dilations, we extend the definition of similarity to figures outside of the coordinate plane. I like to focus on the properties of similar figures – proportional sides, and congruent angles to distinguish them from congruent figures. Then we test two figures to determine if they are similar.
Geometry Interactive Notebook: Similar Triangles
After working on proofs, students are eager to get back to solving equations. When we apply similar triangles, we focus on a few simple steps, and then practice, practice, practice.
For the warm-up on this lesson, I have students examine a proportion written 4 different ways, and ask them which one is incorrect. Students realize that there are multiple ways to correctly write a proportion. I emphasize that their numerators, denominators, and fractions should each have something in common. It could be that they are corresponding sides or from the same triangle. While we are on the topic of applying similar triangles, I also like to include some applied problems involving indirect measurement.
Triangle Similarity Postulate & Theorems
After similar polygons, we narrow our focus to similar triangles. For our geometry interactive notebook page, we examine the postulate and theorems that prove triangles similar. I explain to my students that these are shortcuts to determine the similarity of triangles, rather than check the congruence of every pair of angles and the proportionality of every pair of sides. Then, we practice determining the similarity of triangles.
Geometry Interactive Notebook: Similar Triangle Proofs
After congruent triangle and quadrilateral proofs, students are relieved to learn about similar triangle proofs. Students typically find these proofs easier because they require less steps, and have a single focus – find two pairs of congruent angles. We start by discussing the steps for completing similar triangle proofs, and then complete some practice proofs.
Side-Splitter Theorem
Our last geometry interactive notebook similarity page is dedicated to the Side-Splitter Theorem. Depending on which state you call home, you may be refer to this as the Triangle Proportionality Theorem instead. For this lesson, I introduce the theorem, talk about how the parallel lines make congruent angles, and therefore similar triangles, and then students complete the practice examples.
Geometry Interactive Notebook: Similarity Resources
Are you looking for materials to teach this unit? Look no further! All of the pages you see in my Geometry Interactive Notebook: Similarity are now available. Prior to uploading these pages for your use, I taught each lesson as described above. Some of the pages may not look exactly as they do in this post because they have all been edited and updated. Also, a full answer key for each page is included.
Looking for more resources? Check out my interactive notebook resources page!
