Making Scale Drawings Using the Parallel Method
Dani dilated △ 𝐴𝐵𝐶 from center 𝑂, resulting in △ 𝐴′𝐵′𝐶′. She says that she completed the drawing using parallel lines. How could she have done this? Explain.
a. Use a ruler and setsquare to draw a line through 𝐶 parallel to 𝐴𝐵. What ensures that the line drawn is parallel
b. Use a ruler and setsquare to draw a parallelogram 𝐴𝐵𝐶𝐷 around 𝐴𝐵 and point �
Use the figure below with center 𝑂 and a scale factor of 𝑟 = 2 and the following steps to create a scale drawing using the parallel method.
Step 1. Draw a ray beginning at 𝑂 through each vertex of the figure.
Step 2. Select one vertex of the scale drawing to locate; we have selected 𝐴′. Locate 𝐴′ on 𝑂𝐴 so that 𝑂𝐴 ′ = 2𝑂𝐴.
Step 3. Align the setsquare and ruler as in the image below; one leg of the setsquare should line up with side 𝐴𝐵, and the perpendicular leg should be flush against the ruler.
Step 4. Slide the setsquare along the ruler until the edge of the setsquare passes through 𝐴′. Then, along the perpendicular leg of the setsquare, draw the segment through 𝐴′ that is parallel to𝐴𝐵 until it intersects with 𝑂𝐵, and label this point 𝐵′.
Step 5. Continue to create parallel segments to determine each successive vertex point. In this particular case, the setsquare has been aligned with 𝐴𝐶. This is done because, in trying to create a parallel segment from 𝐵𝐶, the parallel segment was not reaching 𝐵′. This could be remedied with a larger setsquare and longer ruler, but it is easily avoided by working on the segment parallel to 𝐴𝐶 instead.
Step 6. Use your ruler to join the final two unconnected vertices.
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