In triangles A B C and D E F , angles B and E each have measure 27 ° and

Question

In triangles A B C and D E F , angles B and E each have measure 27 &#176; and angles C and F each have measure 41 &#176; . Which additional piece of information is sufficient to determine whether triangle A B C is congruent to triangle D E F ?

Accepted Answer

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 A B C and D E F are similar, where side B C corresponds to side E F . 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 A B C and D E F are congruent, it is sufficient to determine whether sides B C and E F have equal length. Thus, the lengths of B C and E F are sufficient to determine whether triangle A B C is congruent to triangle D E F . 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 A B C and D E F are similar, but not whether they are congruent.

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