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# Similarity Esaay Essay

764 words - 4 pages

It's so cute. After redrawing my first monkey by resizing it, the second monkey is smaller but definitely similar. If two figures are similar, they are the same shape but may be different sizes. Shapes can be made smaller or larger through dilation, a transformation using a scale factor to create a similar image. This is what I have done with my monkey (on the graph paper). My original image, Figure 1, has been shrunk to a smaller and similar image by using a scale factor of ½, as shown in Figure 2, after the dilation. My two monkeys are similar because the ratio of their lengths compared to that of the areas fits the Proportional Perimeters and Areas Theorem. Also, their corresponding ...view middle of the document...

Similarly, all other corresponding angles will also be congruent as the shape has not changed after dilation. And obviously, similar figures will have congruent corresponding angles by definition. By using this, I can prove that my two shapes are similar.

Similar figures also have corresponding lengths that are proportional. I can also use this to prove that my two shapes are similar. By using the distance formula, I can find that the height of Figure 1 from the bottom line to the highest point is 56 units and the width of the bottom line is 32 units. In Figure 2, the length is 28 units and the width is 16 units. The ratio of each original length to the length after dilation is 1 to 2, the scale factor. Therefore, the lengths are proportional to each other.

Also, when two figures are similar, the Proportional Perimeters and Areas Theorem will apply. In this case, I can use this to further prove that my images are similar. If the ratio of the original length to the dilated length is a/b, then the ratio of the perimeters is a/b as well and the ratio of the areas is a^2/b^2....

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