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Determining Similarity and Scale in Geometry Problems

This document explores several geometry questions involving similarity of triangles, scale models, and coordinate transformations. Using principles of similar figures, scale factors, and geometry, readers can solve for unknown values such as dimensions of buildings and triangle coordinates. Specific examples include finding values of x in similar triangles, calculating distances using scale maps, and determining vertex coordinates after dilation. The problems exemplify practical applications of geometric concepts in real-world scenarios.

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Determining Similarity and Scale in Geometry Problems

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  1. Answer: (0, 10) Question: What value of x makes the two rectangles similar? 32 3x + 3 24 5x + 10

  2. Answer: -6 Question: An engineer is given a scale model of a building. The model has a height of 8cm, and a width of 10 cm. The actual building is 20m high. What is the actual width of the building?

  3. Answer:25 meters Question: ∆ABC ~ ∆MLK. What is the value of x? L x + 3 5 A K M 15 C 30 B

  4. Answer:7 Question: The scale of a map is 2.5in: 100 ft. If the distance between the bakery and your house is 25in on the map, how far away is the bakery?

  5. Answer: 1 Question: Find the scale factor for the following similar shapes. 50in 10in OLD NEW

  6. Answer: 6 Question: Find the coordinates for K to make ∆BAC ~ ∆MAK M(14, 0) B(7, 0) A C(0 , 5) K

  7. Answer: (8, 16) Question: Find the value of x. 10 x 10 15

  8. Answer: 12 Question: Let ∆ABC have the coordinates A(0,0), B(0, 5) and C(2, 4). What are the coordinates of C’ for ∆A’B’C’ after a dilation with a scale factor of 4?

  9. Answer: .20 Question: Find the measure of each exterior angle of a regular 30-gon.

  10. Answer:1000ft Question: Find the x-coordinate of the vertex for the following quadratic function.

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