Similarity Applications
A free Geometry lesson from the “Triangles, Similarity, and Trigonometry” unit, with a worked example and practice problems including step-by-step solutions.
Similarity lets you measure hard-to-reach objects with proportional triangles, shadows, maps, and scale drawings. The key is matching corresponding sides correctly. 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
- Use similar triangles in context
- Solve indirect measurement problems
- Apply scale drawings
Worked example
Problem. A 6-foot person casts an 8-foot shadow. A tree casts a 20-foot shadow. How tall is the tree?
- The triangles are similar because the sun angle is the same.
- Set height/shadow = 6/8 = x/20.
- x = 15.
- Connect the result back to Similarity Applications so the geometric relationship is explicit.
Answer: 15 feet
Lesson preview: this page shows 5 practice items. The interactive activity contains 28 practice items and 15 quiz items (typed response and multiple choice). Counts include repeated prompts and variants.
Practice problems
1. A map scale is 1 inch to 5 miles. How many miles are 4 inches?
Show solution
- 4 x 5 = 20.
Answer: 20
2. A 3-foot model represents 18 feet. What is the scale factor from model to real?
Show solution
- 18/3 = 6.
Answer: 6
3. A 5-foot student casts a 7-foot shadow. A flagpole casts a 21-foot shadow. How tall is it?
Show solution
- 21 is 3 times 7, so height is 3 times 5.
Answer: 15
4. A drawing is 8 cm wide and the real object is 32 cm wide. What is the scale factor from drawing to real?
Show solution
- 32/8 = 4.
Answer: 4
5. A 2-inch blueprint length represents 9 feet. What real length does 7 inches represent?
Show solution
- 9/2 = 4.5 feet per inch.
- 7 x 4.5 = 31.5.
Answer: 31.5
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