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Exploring Size Transformations and Proportions in Similar Figures

This worksheet focuses on understanding size transformations, ratios, and proportions through various exercises involving points on a graph and real-life applications. Students will graph two sets of points to visualize changes under size transformations and learn the definitions and examples of ratios and proportions. The tasks include calculating the cost of items based on weight, determining printing times based on rates, and applying the concepts of similar figures to find missing lengths and angles. Suitable for reinforcing geometric concepts and their connection to real-world problems.

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Exploring Size Transformations and Proportions in Similar Figures

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  1. Similar Figures Name:_________________ Date:_____ Group:______ • Do Now: • 1. Let Q = (-3, 4), R = (1, 3), S = (2, -2), and T = (-2, -3). • a. Graph QRST at the right. • b. Give the coordinates of Q’, R’, S’, and T ’, • where Q’R’S’T ’ is the image of QRST • under the size change or size • transformation S2, which means (2x,2y). • Q’ = R ’= • S ’ = T ‘ = • c. Graph Q’R’S’T’. 2. Describe the size transformation, Sk (see p.694) 3. When is a size transformation (see p.693) a. an expansion? b. a contraction? c. the identity transformation?

  2. 4a. What is a ratio? (see p.705) b. Give three examples of ratios. 5a. What is a proportion? (see p.706) b. Give three examples of proportions. c. Write a proportion and label its means and its extremes. 5. ∆AWD is the image of ∆UPO under a size change. Write three equal ratios involving the sides of these triangles. 6. If 2.5 pounds of roast beef cost $9.98, what should 6 pounds of roast beef cost? 7. A computer printer prints 100 pages in 12 minutes. At that rate, how long would it take to print 750 pages?

  3. 8. Anita designed a campaign sign on her computer and printed it out on a sheet of • paper 8.5 in. wide. She took it to a copy store to be made into a poster 18 in. wide. • a. Find the size change factor (ratio) of the enlargement. • b. The lettering on the sign Anita printed is .75 in. • tall. About how tall is it on the poster? • c. If Anita’s sign is 11 in. long, what is the • minimum length the poster can be so that • nothing from the original sign is cut off? 9. Give the similar figures theorem (see p. 713) 10. TILE  WALK, with sides and measures as indicated. Find as many missing lengths and angle measures as possible.

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