diff --git a/题库0.3/Problems.json b/题库0.3/Problems.json index 372a9eb2..6ea8c396 100644 --- a/题库0.3/Problems.json +++ b/题库0.3/Problems.json @@ -4868,7 +4868,7 @@ }, "000177": { "id": "000177", - "content": "如图, 正方体的棱长是$a$, 点$E$、$F$分别是两条棱的中点.\n\\begin{center}\n \\begin{tikzpicture}[thick]\n \\path (0,0) node [below left] {$A$} coordinate (A) --++ (2.5,0) node [below right] {$B$} coordinate (B) --++ (45:{2.5/2}) node [right] {$C$} coordinate (C)\n --++ (0,2.5) node [above right] {$C_1$} coordinate (C1)\n --++ (-2.5,0) node [above left] {$D_1$} coordinate (D1) --++ (225:{2.5/2}) node [left] {$A_1$} coordinate (A1) -- cycle;\n \\path (A) ++ (2.5,2.5) node [right] {$B_1$} coordinate (B1) -- (B) (B1) --++ (45:{2.5/2}) (B1) --++ (-2.5,0);\n \\path [dashed] (A) --++ (45:{2.5/2}) node [left] {$D$} coordinate (D) --++ (2.5,0) (D) --++ (0,2.5);\n \\draw ($(A1)!0.5!(D1)$) node [above left] {$E$} coordinate (E) ($(A1)!0.5!(B1)$) node [above] {$F$} coordinate (F);\n \\fill [gray!30] (B) -- (D) -- (E) -- (F);\n \\draw (B) -- (F) -- (E);\n \\draw [dashed] (B) -- (D) -- (E) (D) -- (C) (D) -- (A) (D) -- (D1);\n \\draw (A) -- (B) -- (C) -- (C1) -- (D1) -- (A1) -- (A) (B1) -- (A1) (B1) -- (C1) (B1) -- (B);\n \\end{tikzpicture}\n\\end{center}\n(1) 求证: 四边形$BDEF$(图中阴影部分)是一个梯形;\\\\\n(2) 求四边形$BDEF$的面积.", + "content": "如图, 正方体的棱长是$a$, 点$E$、$F$分别是两条棱的中点.\n\\begin{center}\n \\begin{tikzpicture}[thick]\n \\path (0,0) node [below left] {$A$} coordinate (A) --++ (2.5,0) node [below right] {$B$} coordinate (B) --++ (45:{2.5/2}) node [right] {$C$} coordinate (C)\n --++ (0,2.5) node [above right] {$C_1$} coordinate (C1)\n --++ (-2.5,0) node [above left] {$D_1$} coordinate (D1) --++ (225:{2.5/2}) node [left] {$A_1$} coordinate (A1) -- cycle;\n \\path (A) ++ (2.5,2.5) node [right] {$B_1$} coordinate (B1) -- (B) (B1) --++ (45:{2.5/2}) (B1) --++ (-2.5,0);\n \\path [dashed] (A) --++ (45:{2.5/2}) node [left] {$D$} coordinate (D) --++ (2.5,0) (D) --++ (0,2.5);\n \\draw ($(A1)!0.5!(D1)$) node [above left] {$E$} coordinate (E) ($(A1)!0.5!(B1)$) node [above] {$F$} coordinate (F);\n \\fill [pattern = north east lines] (B) -- (D) -- (E) -- (F);\n \\draw (B) -- (F) -- (E);\n \\draw [dashed] (B) -- (D) -- (E) (D) -- (C) (D) -- (A) (D) -- (D1);\n \\draw (A) -- (B) -- (C) -- (C1) -- (D1) -- (A1) -- (A) (B1) -- (A1) (B1) -- (C1) (B1) -- (B);\n \\end{tikzpicture}\n\\end{center}\n(1) 求证: 四边形$BDEF$(图中阴影部分)是一个梯形;\\\\\n(2) 求四边形$BDEF$的面积.", "objs": [ "K0605003B", "K0602003B" @@ -4883,7 +4883,8 @@ "usages": [], "origin": "教材复习题", "edit": [ - "20220624\t王伟叶, 余利成" + "20220624\t王伟叶, 余利成", + "20230727\t毛培菁" ], "same": [], "related": [],