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2.8 – Proportions & Similar Figures

Learn how to solve proportions using scale factors and find missing side lengths of similar figures through ratios and proportions. Discover the concept of similar figures and their corresponding angles and sides. Practice examples to enhance your understanding.

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2.8 – Proportions & Similar Figures

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  1. 2.8 – Proportions & Similar Figures “I can solve proportions using scale factors.”“I can find missing side lengths of similar figures.”

  2. VOCABULARY • Similar Figures - Figures that are the same shape, but not the same size. Corresponding angles are equal, but the corresponding sides are proportional. • Scale – the ratio of any length on a drawing to the actual length

  3. Similar Figures This symbol means “similar to” The ratios of all 3 sides are the exact same Each angle is equal to another angle in the same position in the other triangle.

  4. Find the missing sides lengths, a and b.

  5. First, write a ratio you know Find length b on your own 8 . 6.4 Next, write a proportion with a side length you need to find. Last, Cross multiply and solve! 8 = 7 . 6.4 a 8a = 44.8 a = 5.6

  6. Example: Finding the length of a Side of Similar Triangles The two triangles below are similar, determine the length of side x.

  7. Example: Continued

  8. A 5 P 10 R 4 d c B Q 6 C Your Turn: In the figure, the two triangles are similar. What is the length of c?

  9. A 5 P 10 R 4 d c B Q 6 C Your Turn: In the figure, the two triangles are similar. What is the length of d?

  10. The sun’s rays strike the building and the girl at the same angle, forming two similar triangles. How tall is the building if the girl is 5ft? -3ft- -------15ft--------

  11. girl’s shadow = building’s shadow girl’s height building’s height 3 = 15 5 x 3x = 75 x = 25 The building is 25 feet tall.

  12. Thanks a lotThe homeworkOnline assignmentT . Nora Abdelwahab

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