He's so cute. After redrawing my first monkey by scaling it down, the second monkey is smaller but definitely similar. If two figures are similar, they have the same shape but may have different dimensions. Shapes can be shrunk or enlarged through dilation, a transformation that uses a scaling factor to create a similar image. This is what I did with my monkey (on graph paper). My original image, Figure 1, was reduced to a smaller, similar image using a scale factor of ½, as shown in Figure 2, after dilation. My two monkeys are similar because the ratio between their lengths and those of the areas fits the Theorem of Perimeters and Proportional Areas. Furthermore, their corresponding angles are congruent and their corresponding lengths are proportional, proving that they are similar by definition. I can create a dilation by multiplying each coordinate by the scale factor ½, so that the ratio of the images is 1 to 2. For example, the tip of my original monkey's tail is at point 75 (62, 16). Multiplying both x and y values by ½ as shown: (62 * ½, 16 * ½), we get (31.8). (x, y) →...
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