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Understanding Proportions and Similar Figures for Problem Solving

Learn how to apply proportions and analyze similar figures to solve real-world problems. Understand scales, measurements, and ratios for accurate calculations.

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Understanding Proportions and Similar Figures for Problem Solving

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  1. 2-8 Proportions and Similar Figures

  2. Similar Figures: Have the same shape but not necessarily the same size The measures of corresponding angles are equal, and corresponding side lengths are proportional The order of the letters when you name the figures is so important because it tells you which parts of the figure are corresponding parts

  3. In the figure below identify all the corresponding sides and angels

  4. Problem 1: Finding the Length of a Side

  5. Problem 2: Applying Similarity The sun’s rays strike the building and the girl at the same angle, forming two similar triangles shown. How tall is the building

  6. Problem 2: Applying Similarity A man who is 6 feet tall is standing next to a flag pole. The shadow of the man is 3.5 feet and the shadow of the flag pole is 17.5 feet. What is the height of the flagpole?

  7. Scale drawing: a drawing that is similar to an actual object or place (floor plans, blueprints, maps) Scale: the ratio of any length on the drawing to the actual length

  8. Problem 3: Interpreting Scale Drawings What is the actual distance from Jacksonville to Orlando? 1in:110mi

  9. The distance from Jacksonville to Gainesville on the map is about 0.6 in. What is the actual distance? 1in:110mi

  10. Scale Model: a three-dimensional model that is similar to a three-dimensional object

  11. Problem 4: Using Scale Models A giant model heart is shown below. The heart is the ideal size for a man who is 170 ft. tall. About what size would you expect the heart of the man who is 6 ft. tall to be?

  12. A scale model of a building is 6in tall. The scale of the model is 1in:50ft. How tall is the actual building?

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