2. 外语
  3. A、Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient. B、Statement (2) ALONE is sufficient, but statem

A、Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient. B、Statement (2) ALONE is sufficient, but statem

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问题
选项 A、Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B、Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C、BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D、EACH statement ALONE is sufficient.
E、Statements (1) and (2) TOGETHER are NOT sufficient.
答案A
解析 The given information implies that △ABD is similar to △ACE, since ∠ABD and ∠ACE have the same measure and these two triangles share an angle at point A. Therefore, the lengths of corresponding sides of these two triangles are proportional. Using AB = BC, it follows that AC=2(AB), and hence the lengths of the sides of △ACE are twice the lengths of the corresponding sides of △ABD.
(1)     Given that EC = 6, it follows from the remarks above that DB = (1/2)(6) = 3; SUFFICIENT.
(2)     The figure below shows two possibilities satisfying the given information and DE = 5 that have different values for DB; NOT sufficient.

The correct answer is A;
statement 1 alone is sufficient.
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