Proportions and Similar Figures: Understanding Corresponding Parts
Similar figures have the same shape but not size. Their corresponding angles are equal, and side lengths are proportional. Learn about identifying corresponding sides and angles, finding side lengths, applying similarity, interpreting scale drawings, and using scale models in this educational content.
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Presentation Transcript
2-8 Proportions and Similar Figures
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
In the figure below identify all the corresponding sides and angels ABC FGH
Problem 1: Finding the Length of a Side
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
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?
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
Problem 3: Interpreting Scale Drawings What is the actual distance from Jacksonville to Orlando? 1in:110mi
The distance from Jacksonville to Gainesville on the map is about 0.6 in. What is the actual distance? 1in:110mi
Scale Model: a three-dimensional model that is similar to a three- dimensional object
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?
A scale model of a building is 6in tall. The scale of the model is 1in:50ft. How tall is the actual building?
