如圖,正方體
ABCD-
A1B1C1D1的棱長(zhǎng)為1,
P為
BC的中點(diǎn),
Q為線段
CC1上的動(dòng)點(diǎn),過點(diǎn)
A,
P,
Q的平面截該正方體所得的截面記為
S.則下列命題正確的是________(寫出所有正確命題的編號(hào)).

①當(dāng)0<
CQ<

時(shí),
S為四邊形;
②當(dāng)
CQ=

時(shí),
S為等腰梯形;
③當(dāng)

<
CQ<1時(shí),
S為六邊形;
④當(dāng)
CQ=1時(shí),
S的面積為

.
截面
S與
DD1的交點(diǎn)為
M,由平面與平面平行的性質(zhì)定理知
AM∥
PQ,若0<
CQ<

,則
M在線段
DD1上(不包括端點(diǎn))如圖
S為四邊形,命題①正確;當(dāng)
CQ=

時(shí),
M點(diǎn)與
D1重合,四邊形
APQD1為等腰梯形,命題②正確.
③中,當(dāng)

<
CQ<1時(shí),連接
AM交
A1D1于
N,則截面
S為五邊形
APQRN,命題③錯(cuò)誤.

當(dāng)
CQ=1時(shí),截面
S為菱形,其對(duì)角線長(zhǎng)分別為

,

,則
S的面積

·

·

=

,故命題④正確
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正方體

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
為

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
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①當(dāng)
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