2.2.2 Applications of Proportion
Key Objectives • Write and solve proportions to find unknown measures in similar figures. • Determine the effects on area, perimeter, and volume when the dimensions of a figure are changed. Key Terms • Similar figures have the same shape but not necessarily the same size.
A pair of corresponding sides of two figures are the sides that are in the same relative position. A pair of corresponding angles of two figures are the angles that are in the same relative position. Two figures are similar if and only if the lengths of the corresponding sides are proportional and all pairs of corresponding angles have equal measures. The statement △ ABC ~ △ DEF means that △ ABC is similar to △ DEF . Therefore, ratios of the corresponding sides of △ ABC and △ DEF are proportional. = = Example 1 Finding Missing Measures in Similar Figures In Example 1, Prof. Burger uses the fact that corresponding sides of similar triangles are proportional to find an unknown side length in one of the triangles. AB DE BC EF AC DF
Example 2 Measurement Application Indirect measurement (a method of measurement where a proportion involving sides of similar triangles is used to find a length that is not easily measured) is demonstrated in Example 2. For this example, assume that the child and the totem pole form right angles with the ground, and that their shadows are cast at the same angle. Two similar right triangles are formed where the heights of the child and pole and the lengths of their shadows are the legs of the triangles.
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