[求助]GWD29-2 數學題DS

Q2:

[attachimg]49007[/attachimg]

In the figure above, is quadrilateral PQRS a parallelogram?
    

(1)       The area of ∆PQS is equal to the area of ∆QRS.

(2)       QR = RS

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.

Answer: E

請教思路,謝謝^_^

請教思路,謝謝^_^

List the properties of a parallelogram and figure out what you need.

Figure out how to calculate ∆PQS  and ∆QRS, and what you can deduce from that.  See if that combined with the second condition is sufficient to conclude the quadrilateral is a parallelogram.

答案是Ｅ，我觉得是Ｃ。求教

(1)面積相同，假設他們共用QS為底，高相同，可是如果將其中一個高，沿著QS左右平移，那其中一個三角形便會變形，因此不一定平行。

(2)QR等於RS，並不代表QP等於PS

(1)(2)合併

同(1)的道理，將QPS的高，沿著QS平移，也可使三角形QPS變形，雖然QR等於RS，也無法證明是平行四邊形。

答案E

(1)+(2)也有可能是菱形