Day 28 of 30
Dilations and similarity
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Learning Objective
Students will explore dilations and similarity through guided practice and application.
This lesson focuses on dilations and similarity. Mathematics provides tools for modeling and analyzing complex systems.
Similar figures have the same shape but not necessarily the same size—corresponding angles are equal and corresponding sides are proportional. Scale factor k: ratio of corresponding lengths. For triangles: AA (two angles), SSS (sides proportional), SAS (two sides and included angle proportional). Similarity is used for indirect measurement, scale drawings, and proofs!
As you engage with this material, consider both the theoretical foundations and practical applications. Think critically about how this concept builds on prior knowledge and where you might apply it beyond the classroom.
Challenge yourself to go beyond memorization—seek to understand the "why" behind the processes and principles.
A mathematical question requiring analysis and solution
The result obtained by solving a problem
Instructions
Materials Needed
- Notebook
- Calculator (if needed)
- Graph paper
Two similar triangles have scale factor 3. If a side in the smaller is 4, find the corresponding side in the larger.
Similar figures: scale factor 2. How does area change?
Scale factor 1/2. If a length in the original is 10, what is it in the image?
Teaching Tip
For advanced learners: Encourage deeper analysis and real-world connections. Consider extension activities that allow students to apply dilations and similarity to novel situations.