Builders and architects use scale models to help them design and build new buildings. An architecture student builds a model of an office building in which the height of the model is times the height of
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the actual building, while the width and length of the model are each times the corresponding
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dimensions of the actual building. The model includes several triangles. Could a triangle in the model be
similar to a corresponding triangle in the actual building? Could a triangle in the model not be similar to a
triangle in the actual building? Complete the explanation.
A triangle that has vertices at one height only, meaning it is parallel to the ground, will have side lengths
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that are each times the side lengths of the corresponding triangle in the actual building. The two
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triangles are similar by the ? Triangle Similarity Theorem. A triangle that has vertices at several
heights will? have side lengths that form a constant ratio with the side lengths of the
corresponding triangle in the actual building. These triangles will ? be similar