## Working with Similar Figures - Section 1: Linking Dilations to Similar Figures

# Introduction to Similar Figures

Lesson 1 of 9

## Objective: Students will be able to understand the relationships between the sides and the angles of similar figures.

*45 minutes*

I begin by asking the students to plot a quadrilateral on their graph paper and to record the coordinates of the vertices. I then ask them to think back to our unit on Transformations, and to perform a dilation that I specify on their quadrilateral. Then, I will ask the class to share information about the results of their dilation of the quadrilateral:

- Are their pre-image and image congruent? Why or why not?
- What remained invariant in their figures? Why? What changed and how?

The change in the lengths of sides is easy for the students to see and comprehend. **The invariance of the angles is not so obvious to many of the students, however, and needs to be emphasized**. Often students expect, for example, that if the sides double, the angles will double, too.

It is at this point, I introduce the term **similar** to describe their figures (image and preimage).

#### Resources

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Students are given Similar Polygons. I lead them through the notes, giving them time to work in their groups to complete each section of problems. I then allow the groups to compare answers with their neighbors, we discuss any differences in their answers, and move on to the next section of problems.

This series of problems presents students with a summary of the concepts. It requires them to complete numerical problems involving proportions. Finally, it asks students to reflect and to make observations based on their solutions. For example:

- How is scale factor related to perimeters of similar figures?
- Are all quadrilaterals similar? If not, are there quadrilaterals that are always similar?

The section of "Always, Sometimes, Never" questions is always tough for the majority of my students, and will require a good deal of class discussion, examples, and counterexamples.

#### Resources

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#### Lesson End + Homework

*2 min*

For Homework, the students are asked to complete the final three problems in the Similar Polygons notes (see Page 4). I remind them to refer back to the class notes if they struggle with the homework problems. It is my hope that these problems will provide enough practice to keep the concepts fresh in students' minds so they are ready for the next day’s lesson.

To help me assess their understanding of this lesson, I give a **Ticket out the Door**, asking the students to briefly explain the differences between similar and congruent figures in their own words.

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*Responding to Tess Schmidt*

Thank you! I'm glad this was helpful.

| 8 months ago | Reply

Thank you! My students understood this much more clearly! You work was clear and well thought out.

| 8 months ago | Reply

The TUNE ~ T'U'N'E example on the Similar Polygons resource is inaccurate. Students are asked what type of quadrilateral these shapes must be, at which point students identify them as trapezoids because same-side interior angles are supplementary, but then when students find UN and T'E' they notice the shape is more accurately an isosceles trapezoid. This does not work with the figure as describe though, because the base angles are not congruent.

To fix this, a more appropriate length for U'N' would be 17.6, making UN 22.

| 11 months ago | Reply

Beth, this lesson is great. The objective is clear and the components of the lesson are very straight forward and engaging. Great planning. Thanks for sharing.

| 2 years ago | Reply

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- LESSON 1: Introduction to Similar Figures
- LESSON 2: Similar Figures Activity
- LESSON 3: Create Your Own Similar Figures
- LESSON 4: Proving that Triangles are Similar
- LESSON 5: Working with Similar Triangles
- LESSON 6: Working with Similar Triangles, Part 2
- LESSON 7: Error Analysis: Finding Sides of Similar Triangles
- LESSON 8: Pulling It All Together (Part 1)
- LESSON 9: Pulling It All Together (Part 2)