- - - -_DEF_,_angles_B_and_E_each - - - - ABC In triangles and have measure 27° and angles C and F each have 41° measure. Which additional piece of information ABC is sufficient to determine whether triangle is DEF congruent to triangle?
Correct answer: C (parsed from the explanation — this source omits an answer key for this item)
Explanation
Choice C is correct. Since angles B and E each have the same measure and angles C and F each have the same measure, triangles ABC and DEF are similar, where side BC corresponds to side EF. To determine whether two similar triangles are congruent, it is sufficient to determine whether one pair of corresponding sides are congruent. Therefore, to determine whether triangles ABC and DEF are congruent, it is sufficient to determine whether sides BC and EF have equal length. Thus, the lengths of BC and EF are sufficient to determine whether triangle ABC is congruent to triangle DEF. Choice A is incorrect and may result from conceptual errors. Choice B is incorrect and may result from conceptual errors. Choice D is incorrect. The given information is sufficient to determine that triangles ABC and DEF are similar, but not whether they are congruent.
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