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Lines, angles, and triangles SAT question

Math · Geometry and Trigonometry · Medium · Answer it here, explanation included.

Triangle is similar to triangle , such that , , and correspond to , , and respectively. The length of each side of triangle is times the length of its corresponding side in triangle . The measure of side is . What is the measure of side ?

ExplanationShow

Choice D is correct. It's given that triangle  is similar to triangle , such that , , and correspond to , , and , respectively. Therefore, side corresponds to side . Since the length of each side of triangle is times the length of its corresponding side in triangle , it follows that the measure of side is times the measure of side . Thus, since the measure of side is , then the measure of side is , or .

Choice A is incorrect and may result from conceptual or calculation errors.

Choice B is incorrect. This is the measure of side , not side .

Choice C is incorrect and may result from conceptual or calculation errors.

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