题目信息
In the figure above, B is on
, D is on 
, 
has the same length as 
, and 
has the same measure as 
. What is the length of 
?
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.
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已选答案：
正确答案：
A:Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
Geometry Triangles
The given information implies that ΔABD is similar to ΔACE, 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 ΔACE are twice the lengths of the corresponding sides of ΔABD.
Given that EC = 6, it follows from the remarks above that
; SUFFICIENT.
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.
The given information implies that ΔABD is similar to ΔACE, 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 ΔACE are twice the lengths of the corresponding sides of ΔABD.Given that EC = 6, it follows from the remarks above that
; SUFFICIENT.
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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