Geometry 10-4 Perimeters of Areas of Similar Figures

by Matthew Richardson

| 24 QuestionsNote from the author:

A complete formative lesson with embedded slideshow, mini lecture screencasts, checks for understanding, practice items, mixed review, and reflection. I create these assignments to supplement each lesson of Pearson's Common Core Edition Algebra 1, Algebra 2, and Geometry courses. See also mathquest.net and twitter.com/mathquestEDU.

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10 pts

Solve It! Complete the tables on the canvas using the text tool.

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Solve It! How do the ratios of the perimeters and the ratios of the areas compare with the scale factors?

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10 pts

Problem 1 Got It?

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Problem 1 Got It?

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10 pts

Problem 2 Got It?

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10 pts

Problem 3 Got It? The scale factor of the dimensions of two small pieces of window glass is 3 : 5. The smaller piece costs $2.50. How much should the larger piece cost?

Enter your answer in this format: $2.71

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10 pts

Problem 3 Got It? Reasoning: In Problem 3, why is it important that each dimension is 2.5 times the corresponding dimension of the original plot? Explain.

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10 pts

Problem 4 Got It?

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10 pts

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10 pts

Reasoning: The area of one rectangle is twice the area of a similar rectangle. What is the ratio of their perimeters? How do you know?

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10 pts

Error Analysis: Your friend says that since the ratio of the perimeters of two polygons is ½, the area of the smaller polygon must be one half the area of the larger polygon. What is wrong with this statement? Explain.

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10 pts

Compare and Contrast: How is the relationship between the areas of two congruent figures different from the relationship between the areas of two similar figures?

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10 pts

Review Lesson 10-3: Match each regular polygon with its area.

- 480 square units
- 690 square units
- 484 square units

- a square with apothem 11
- a regular pentagon with apothem 13.8 and side length 20
- an octagon with apothem 12 and side length 10

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10 pts

Review Lesson 10-3: Fill in the blank. Enter only a number. The area of the regular polygon is __?__ square inches.

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10 pts

Vocabulary Review: Categorize each statement based on whether it is always, sometimes, or never true.

- Corresponding angles of similar figures are congruent.
- Corresponding sides of similar figures are proportional.

- Always
- Sometimes
- Never

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10 pts

Vocabulary Review: Identify the pairs of similar figures. Select all that apply.

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10 pts

Use Your Vocabulary: Which segment is NOT a radius of regular pentagon ABCDE?

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10 pts

Use Your Vocabulary: Complete each sentence with are or are not.

- are
- are not

- The radii of a regular polygon __?__ congruent.
- The triangles formed by the radii and sides of regular pentagon ABCD __?__ congruent.

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10 pts

Reflection: Math Success

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