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Goals : Find the perimeters and areas of similar figures.

Chapter 8: Similarity Lesson 8-6: Perimeters and Areas of Similar Figures Lesson 10-8: Areas and Volumes of Similar Solids. Goals : Find the perimeters and areas of similar figures. Find relationships between the ratios of the areas and volumes of similar solids.

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Goals : Find the perimeters and areas of similar figures.

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  1. Chapter 8: SimilarityLesson 8-6: Perimeters and Areas of Similar FiguresLesson 10-8: Areas and Volumes of Similar Solids Goals: Find the perimeters and areas of similar figures. Find relationships between the ratios of the areas and volumes of similar solids.

  2. Perimeters and Areas of Similar Figures: • Theorem 8-6 – Perimeters and Areas of Similar Figures: If the similarity ratio of two similar figures is a:b, then • (1) the ratio of their perimeters is a:b, and • (2) the ratio of their areas is a2:b2.

  3. similar solids: • similar solids: Similar solids have the same shape, and all of their corresponding dimensions are proportional.

  4. similarity ratio for solids: • similarity ratio: The ratio of corresponding linear dimensions of two solids is the similarity ratio. • Just as any two squares are similar, so are any two cubes; also, just as any two circles are similar, so are any two spheres.

  5. Areas and Volumes of Similar Solids: • Theorem 10-12 – Areas and Volumes of Similar Solids: If the similarity ratio of two similar solids is a:b, then • (1) the ratio of their corresponding areas is a2:b2, and • (2) the ratio of their corresponding volumes is a3:b3.

  6. Examples: • Exercises 8-6 #2, 8, 36:

  7. Examples: • Exercises 10-8 #2, 4, 16:

  8. Assignments: • CW: Practice 8-6/10-8. • HW 8-6: #3-21 (every 3rd), 35, 37 and 10-8: #3-18 (every 3rd), 30-34. • Bring geometry tools and a calculator to class. Final Thursday, January 26.

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