Similar Triangles and Scale Factor
A free Geometry lesson from the “Triangles, Similarity, and Trigonometry” unit, with a worked example and practice problems including step-by-step solutions.
Similar triangles have the same shape but not necessarily the same size. Corresponding angles are congruent, and corresponding side lengths are proportional. In Triangles, Similarity, and Trigonometry, students need to read the diagram, name the relationship, choose a theorem or formula, and justify why the result follows. The expanded practice now includes fluency, transfer, cumulative review, and proof-style reasoning so Geometry feels connected instead of isolated by topic.
What you'll learn
- Identify similar triangles
- Use scale factors
- Find missing side lengths
Worked example
Problem. Two similar triangles have corresponding sides 4 and 10. A second side in the smaller triangle is 6. Find the matching larger side.
- The scale factor is 10/4 = 2.5.
- Multiply the smaller side by 2.5.
- 6 x 2.5 = 15.
- Connect the result back to Similar Triangles and Scale Factor so the geometric relationship is explicit.
Answer: 15
Lesson preview: this page shows 5 practice items. The interactive activity contains 28 practice items and 15 quiz items (multiple choice and typed response). Counts include repeated prompts and variants.
Practice problems
1. Similar triangles have corresponding angles that are...
Choices: Congruent · Supplementary · Always right · Different
Show solution
- Similar figures have equal corresponding angles.
Answer: Congruent
2. A side of 5 scales by factor 3. What is the new length?
Show solution
- 5 x 3 = 15.
Answer: 15
3. Two similar triangles have sides 4 and 12. What is the scale factor from smaller to larger?
Show solution
- 12/4 = 3.
Answer: 3
4. A smaller triangle side is 7 and scale factor is 2. What is the larger side?
Show solution
- 7 x 2 = 14.
Answer: 14
5. Matching sides are 6 and 9. A smaller side is 10. What is the larger matching side?
Show solution
- Scale factor is 9/6 = 1.5.
- 10 x 1.5 = 15.
Answer: 15
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