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Proportions and Exploring Similar Triangles

Proportions and Exploring Similar Triangles. Sec: 7.1 and 7.2. Have you ever looked on a map to see how far it was between two different locations? Most often we can measure this distance and use a scale to convert to miles. The scale is usually found in the legend of the map.

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Proportions and Exploring Similar Triangles

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  1. Proportions and Exploring Similar Triangles Sec: 7.1 and 7.2

  2. Have you ever looked on a map to see how far it was between two different locations? Most often we can measure this distance and use a scale to convert to miles. The scale is usually found in the legend of the map. This kind of scale is also called a ratio.

  3. A ratio is a ____________________________ of two quantities. The ratio of a to b can be expressed as , where . The ratio can also be written as a : b . Example: Express the number of girls to the number of boys in this class as a ratio: • _______ to _______ or • _______ : _______ or • _________ (as a fraction, which can be simplified)

  4. An equation stating that two ratios are equal is a Proportion. Example: Solve by Cross Products:

  5. Solve the following Proportions:

  6. Ratio word problems

  7. Ex: 1 A box car on a train has a length of 40 ft and a width of 9 ft. A scale model is made with a length of 16 inches. Find the width of the model.

  8. Example 2 • The ratio of sophomores to freshmen on the football team is 4:5. If there are 40 freshmen, how many sophomores are there?

  9. Example 3 • A 20 foot building casts a 12 foot shadow. How tall is a building that casts a 30 foot shadow at the same time?

  10. 7.2 Exploring Similar Polygons When figures have the same shape but are different sizes, they are called similar polygons. Definition of Similar Polygons: Two polygons are similar iff their corresponding angles are congruent and the measures of their corresponding sides are proportional.

  11. The ratio of the lengths of two corresponding sides of two similar polygons is called the scale factor. • In the previous example, what is the scale factor of quadrilateral ABCD to quadrilateral EFGH? • In the previous example, what is the scale factor of quadrilateral EFGH to quadrilateral ABCD?

  12. Example 4

  13. Example 5 6 4 • Find the Scale Factor: • Find x: • Find y: • Find : x 3 y+1 8

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