diff --git a/工具/分年级专用工具/讲义题目分类按顺序梳理_制答题卡用.ipynb b/工具/分年级专用工具/讲义题目分类按顺序梳理_制答题卡用.ipynb
index 9bc3ef85..e3e101f4 100644
--- a/工具/分年级专用工具/讲义题目分类按顺序梳理_制答题卡用.ipynb
+++ b/工具/分年级专用工具/讲义题目分类按顺序梳理_制答题卡用.ipynb
@@ -2,52 +2,42 @@
  "cells": [
   {
    "cell_type": "code",
-   "execution_count": 1,
+   "execution_count": 2,
    "metadata": {},
    "outputs": [
     {
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "1 解答题 1\n",
+      "1 选择题 1\n",
       "2 解答题 1\n",
       "3 解答题 1\n",
       "4 解答题 1\n",
-      "5 填空题 2\n",
-      "6 解答题 2\n",
-      "7 填空题 10\n",
-      "8 解答题 1\n",
-      "9 解答题 1\n",
-      "10 解答题 1\n",
+      "5 解答题 1\n",
+      "6 解答题 4\n",
+      "7 填空题 4\n",
+      "8 填空题 1\n",
+      "9 填空题 1\n",
+      "10 解答题 2\n",
       "11 解答题 1\n",
       "12 解答题 1\n",
-      "13 填空题 6\n",
+      "13 解答题 1\n",
       "14 解答题 1\n",
-      "15 填空题 1\n",
-      "16 解答题 1\n",
-      "17 填空题 3\n",
-      "18 填空题 1\n",
-      "19 填空题 1\n",
-      "1 解答题 2\n",
-      "2 解答题 1\n",
-      "3 填空题 6\n",
-      "4 填空题 1\n",
-      "5 选择题 1\n",
-      "6 选择题 1\n",
-      "7 填空题 2\n",
-      "8 解答题 1\n",
-      "9 解答题 1\n",
-      "10 解答题 1\n",
-      "11 解答题 1\n",
-      "12 解答题 2\n",
-      "13 解答题 1\n"
+      "15 解答题 4\n",
+      "1 解答题 5\n",
+      "2 选择题 1\n",
+      "3 解答题 1\n",
+      "4 解答题 1\n",
+      "5 解答题 2\n",
+      "6 解答题 1\n",
+      "7 填空题 1\n"
      ]
     }
    ],
    "source": [
     "import os,re\n",
     "#修改文件名\n",
-    "filename = r\"C:\\Users\\Wang Weiye\\Documents\\wwy sync\\23届\\第一轮复习讲义\\20_描述空间位置关系的公理.tex\"\n",
+    "filename = r\"C:\\Users\\Wang Weiye\\Documents\\wwy sync\\23届\\第一轮复习讲义\\22_空间平面与平面的位置关系.tex\"\n",
     "# filename = r\"C:\\Users\\Wang Weiye\\Documents\\wwy sync\\23届\\上学期周末卷\\国庆卷.tex\"\n",
     "outputfile = \"临时文件/题目状态.txt\"\n",
     "\n",
diff --git a/工具/添加关联题目.ipynb b/工具/添加关联题目.ipynb
index 4ee73481..f2bfa97e 100644
--- a/工具/添加关联题目.ipynb
+++ b/工具/添加关联题目.ipynb
@@ -2,15 +2,15 @@
  "cells": [
   {
    "cell_type": "code",
-   "execution_count": 2,
+   "execution_count": 8,
    "metadata": {},
    "outputs": [],
    "source": [
     "import os,re,json,time\n",
     "\n",
     "\"\"\"---设置原题目id与新题目id---\"\"\"\n",
-    "old_id = \"1598\"\n",
-    "new_id = \"30112\"\n",
+    "old_id = \"9697\"\n",
+    "new_id = \"30151\"\n",
     "\"\"\"---设置完毕---\"\"\"\n",
     "\n",
     "old_id = old_id.zfill(6)\n",
diff --git a/工具/讲义生成.ipynb b/工具/讲义生成.ipynb
index 9b36b4ca..b4671188 100644
--- a/工具/讲义生成.ipynb
+++ b/工具/讲义生成.ipynb
@@ -2,7 +2,7 @@
  "cells": [
   {
    "cell_type": "code",
-   "execution_count": 3,
+   "execution_count": 4,
    "metadata": {},
    "outputs": [
     {
@@ -13,11 +13,9 @@
       "题块 1 处理完毕.\n",
       "正在处理题块 2 .\n",
       "题块 2 处理完毕.\n",
-      "正在处理题块 3 .\n",
-      "题块 3 处理完毕.\n",
-      "开始编译教师版本pdf文件:  临时文件/周末卷04_教师_20221010.tex\n",
+      "开始编译教师版本pdf文件:  临时文件/22_空间平面与平面的位置关系_教师_20221011.tex\n",
       "0\n",
-      "开始编译学生版本pdf文件:  临时文件/周末卷04_学生_20221010.tex\n",
+      "开始编译学生版本pdf文件:  临时文件/22_空间平面与平面的位置关系_学生_20221011.tex\n",
       "0\n"
      ]
     }
@@ -30,19 +28,19 @@
     "\"\"\"---设置模式结束---\"\"\"\n",
     "\n",
     "\"\"\"---设置模板文件名---\"\"\"\n",
-    "# template_file = \"模板文件/第一轮复习讲义模板.tex\"\n",
-    "template_file = \"模板文件/测验周末卷模板.tex\"\n",
+    "template_file = \"模板文件/第一轮复习讲义模板.tex\"\n",
+    "# template_file = \"模板文件/测验周末卷模板.tex\"\n",
     "# template_file = \"模板文件/日常选题讲义模板.tex\"\n",
     "\"\"\"---设置模板文件名结束---\"\"\"\n",
     "\n",
     "\"\"\"---设置其他预处理替换命令---\"\"\"\n",
     "#2023届第一轮讲义更换标题\n",
-    "# exec_list = [(\"标题数字待处理\",\"20\"),(\"标题文字待处理\",\"描述空间位置关系的公理\")] \n",
-    "# enumi_mode = 0\n",
+    "exec_list = [(\"标题数字待处理\",\"21\"),(\"标题文字待处理\",\"空间平面与平面的位置关系\")] \n",
+    "enumi_mode = 0\n",
     "\n",
     "#2023届测验卷与周末卷\n",
-    "exec_list = [(\"标题替换\",\"周末卷04\")]\n",
-    "enumi_mode = 1\n",
+    "# exec_list = [(\"标题替换\",\"周末卷04\")]\n",
+    "# enumi_mode = 1\n",
     "\n",
     "#日常选题讲义\n",
     "# exec_list = [(\"标题文字待处理\",\"2022年国庆卷(易错题订正)\")] \n",
@@ -51,15 +49,14 @@
     "\"\"\"---其他预处理替换命令结束---\"\"\"\n",
     "\n",
     "\"\"\"---设置目标文件名---\"\"\"\n",
-    "destination_file = \"临时文件/周末卷04\"\n",
+    "destination_file = \"临时文件/22_空间平面与平面的位置关系\"\n",
     "\"\"\"---设置目标文件名结束---\"\"\"\n",
     "\n",
     "\n",
     "\"\"\"---设置题号数据---\"\"\"\n",
     "problems = [\n",
-    "\"1853,30108,3355,655,724,1860,2038,30106,30107,3621\",\n",
-    "\"1846,2013,3703\",\n",
-    "\"1557,4702\"\n",
+    "'1649,30095,30144,30096,30100,9698,3499,1665,1659,303,30097,30145,188,9700',\n",
+    "\"9697,9158,1645,189,9154,1704,1670,294\"\n",
     "]\n",
     "\"\"\"---设置题号数据结束---\"\"\"\n",
     "\n",
diff --git a/工具/题号选题pdf生成.ipynb b/工具/题号选题pdf生成.ipynb
index ac4cacc4..fe5f5990 100644
--- a/工具/题号选题pdf生成.ipynb
+++ b/工具/题号选题pdf生成.ipynb
@@ -2,16 +2,16 @@
  "cells": [
   {
    "cell_type": "code",
-   "execution_count": 4,
+   "execution_count": 5,
    "metadata": {},
    "outputs": [
     {
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "开始编译教师版本pdf文件:  临时文件/多面体与旋转体选题_教师用_20221010.tex\n",
+      "开始编译教师版本pdf文件:  临时文件/多面体与旋转体选题_教师用_20221011.tex\n",
       "0\n",
-      "开始编译学生版本pdf文件:  临时文件/多面体与旋转体选题_学生用_20221010.tex\n",
+      "开始编译学生版本pdf文件:  临时文件/多面体与旋转体选题_学生用_20221011.tex\n",
       "0\n"
      ]
     }
@@ -26,7 +26,7 @@
     "\"\"\"---设置题目列表---\"\"\"\n",
     "#留空为编译全题库, a为读取临时文件中的题号筛选.txt文件生成题库\n",
     "problems = r\"\"\"\n",
-    "a\n",
+    "30146:30151\n",
     "\n",
     "\"\"\"\n",
     "\"\"\"---设置题目列表结束---\"\"\"\n",
diff --git a/题库0.3/LessonObj.json b/题库0.3/LessonObj.json
index 66580edb..66d38ff5 100644
--- a/题库0.3/LessonObj.json
+++ b/题库0.3/LessonObj.json
@@ -2552,7 +2552,7 @@
     "K0617006B": {
         "id": "K0617006B",
         "unit_obj": "D06006B",
-        "content": "能用直圆柱的侧面积公式和表面积公式计算数学情境或现实情境中的直棱柱的侧面积与表面积."
+        "content": "能用圆柱的侧面积公式和表面积公式计算数学情境或现实情境中的圆柱的侧面积与表面积."
     },
     "K0617007B": {
         "id": "K0617007B",
@@ -2637,7 +2637,7 @@
     "K0620004B": {
         "id": "K0620004B",
         "unit_obj": "D06006B",
-        "content": "会在简单的具体情境中计算锥体的表面积."
+        "content": "会在简单的具体情境中计算锥体的侧面积与表面积."
     },
     "K0620005B": {
         "id": "K0620005B",
diff --git a/题库0.3/Problems.json b/题库0.3/Problems.json
index 52be559d..e7079f9f 100644
--- a/题库0.3/Problems.json
+++ b/题库0.3/Problems.json
@@ -4520,7 +4520,9 @@
             "20220624\t王伟叶, 余利成"
         ],
         "same": [],
-        "related": [],
+        "related": [
+            "030148"
+        ],
         "remark": "",
         "space": "12ex"
     },
@@ -41730,7 +41732,7 @@
     },
     "001620": {
         "id": "001620",
-        "content": "正方体$ABCD-A'B'C'D'$中, 求证:\\\\ \n(1) $D'B\\perp AC$;\\\\ \n(2) $D'B\\perp$平面$AB'C$. \n\\begin{center}\n\\begin{tikzpicture}\n    \\draw (0,0) node [below left] {$A$} coordinate (A) --++ (3,0) node [below right] {$B$} coordinate (B) --++ (45:{3/2}) node [right] {$C$} coordinate (C)\n    --++ (0,3) node [above right] {$C'$} coordinate (C1)\n    --++ (-3,0) node [above left] {$D'$} coordinate (D1) --++ (225:{3/2}) node [left] {$A'$} coordinate (A1) -- cycle;\n    \\draw (A) ++ (3,3) node [right] {$B'$} coordinate (B1) -- (B) (B1) --++ (45:{3/2}) (B1) --++ (-3,0);\n    \\draw [dashed] (A) --++ (45:{3/2}) node [left] {$D$} coordinate (D) --++ (3,0) (D) --++ (0,3);\n    \\draw (A) -- (B1) -- (C);\n    \\draw [dashed] (A) -- (C) (B) -- (D1);\n\\end{tikzpicture}\n\\end{center}",
+        "content": "正方体$ABCD-A'B'C'D'$中, 求证:\\\\ \n(1) $D'B\\perp AC$;\\\\ \n(2) $D'B\\perp$平面$AB'C$. \n\\begin{center}\n\\begin{tikzpicture}[scale = 0.5]\n    \\draw (0,0) node [below left] {$A$} coordinate (A) --++ (3,0) node [below right] {$B$} coordinate (B) --++ (45:{3/2}) node [right] {$C$} coordinate (C)\n    --++ (0,3) node [above right] {$C'$} coordinate (C1)\n    --++ (-3,0) node [above left] {$D'$} coordinate (D1) --++ (225:{3/2}) node [left] {$A'$} coordinate (A1) -- cycle;\n    \\draw (A) ++ (3,3) node [right] {$B'$} coordinate (B1) -- (B) (B1) --++ (45:{3/2}) (B1) --++ (-3,0);\n    \\draw [dashed] (A) --++ (45:{3/2}) node [left] {$D$} coordinate (D) --++ (3,0) (D) --++ (0,3);\n    \\draw (A) -- (B1) -- (C);\n    \\draw [dashed] (A) -- (C) (B) -- (D1);\n\\end{tikzpicture}\n\\end{center}",
         "objs": [
             "K0611002B"
         ],
@@ -42251,7 +42253,7 @@
     },
     "001641": {
         "id": "001641",
-        "content": "已知$PA\\perp$三角形$ABC$所在平面, 且$AB=AC=13$, $BC=10$, $PA=12$, $D$是$BC$中点.\\\\ \n(1) 求直线$PD$与平面$ABC$所成角的大小;\\\\ \n(2) 求直线$PC$与平面$PAD$所成角的正切;\\\\ \n(3) 求直线$PC$与平面$PAB$所成角的正切.",
+        "content": "已知$PA\\perp$三角形$ABC$所在平面, 且$AB=AC=13$, $BC=10$, $PA=12$, $D$是$BC$中点.\\\\ \n(1) 求直线$PD$与平面$ABC$所成角的大小;\\\\ \n(2) 求直线$PC$与平面$PAD$所成角的正切值;\\\\ \n(3) 求直线$PC$与平面$PAB$所成角的正切值.",
         "objs": [
             "K0610004B"
         ],
@@ -42453,7 +42455,7 @@
     },
     "001649": {
         "id": "001649",
-        "content": "下列命题中不正确的是\\bracket{20}.\\\\ \n\\onech{垂直于同一条直线的两个平面平行}{垂直于同一个平面的两条直线相互平行}{若一个平面内有无数条直线都平行于另一个平面, 则这两个平面互相平行}{若两个平行平面分别和第三个平面相交, 则它们的交线互相平行}",
+        "content": "下列命题中不正确的是\\bracket{20}.\n\\onech{垂直于同一条直线的两个平面平行}{垂直于同一个平面的两条直线相互平行}{若一个平面内有无数条直线都平行于另一个平面, 则这两个平面互相平行}{若两个平行平面分别和第三个平面相交, 则它们的交线互相平行}",
         "objs": [
             "K0612001B"
         ],
@@ -42863,7 +42865,9 @@
             "20220625\t王伟叶"
         ],
         "same": [],
-        "related": [],
+        "related": [
+            "030146"
+        ],
         "remark": "",
         "space": ""
     },
@@ -105871,7 +105875,7 @@
     },
     "004283": {
         "id": "004283",
-        "content": "在正方体$ABCD-A_1B_1C_1D_1$中, $P$、$Q$两点分别从点$B$和点$A_1$出发, 以相同的速度在棱$BA$和$A_1D_1$上运动至点$A$和点$D_1$, 在运动过程中, 直线$PQ$与平面$ABCD$所成角$\\theta$的变化范围为\\bracket{20}.\n\\begin{center}\n    \\begin{tikzpicture}\n        \\draw (0,0) node [below left] {$A$} coordinate (A) --++ (2,0) node [below right] {$B$} coordinate (B) --++ (45:{2/2}) node [right] {$C$} coordinate (C)\n        --++ (0,2) node [above right] {$C_1$} coordinate (C1)\n        --++ (-2,0) node [above left] {$D_1$} coordinate (D1) --++ (225:{2/2}) node [left] {$A_1$} coordinate (A1) -- cycle;\n        \\draw (A) ++ (2,2) node [right] {$B_1$} coordinate (B1) -- (B) (B1) --++ (45:{2/2}) (B1) --++ (-2,0);\n        \\draw [dashed] (A) --++ (45:{2/2}) node [left] {$D$} coordinate (D) --++ (2,0) (D) --++ (0,2);\n        \\draw [dashed] ($(A1)!0.3!(D1)$) node [above left] {$Q$} -- ($(B)!0.3!(A)$) node [below] {$P$};\n    \\end{tikzpicture}\n\\end{center}\n\\twoch{$[\\dfrac\\pi4,\\dfrac\\pi3]$}{$[\\arctan\\dfrac{\\sqrt{2}}2,\\arctan\\sqrt 2]$}{$[\\dfrac\\pi4,\\arctan\\sqrt 2]$}{$[\\arctan\\dfrac{\\sqrt{2}}2,\\dfrac\\pi2]$}",
+        "content": "在正方体$ABCD-A_1B_1C_1D_1$中, $P$、$Q$两点分别从点$B$和点$A_1$出发, 以相同的速度在棱$BA$和$A_1D_1$上运动至点$A$和点$D_1$, 在运动过程中, 直线$PQ$与平面$ABCD$所成角$\\theta$的变化范围为\\bracket{20}.\n\\begin{center}\n    \\begin{tikzpicture}[scale = 0.7]\n        \\draw (0,0) node [below left] {$A$} coordinate (A) --++ (2,0) node [below right] {$B$} coordinate (B) --++ (45:{2/2}) node [right] {$C$} coordinate (C)\n        --++ (0,2) node [above right] {$C_1$} coordinate (C1)\n        --++ (-2,0) node [above left] {$D_1$} coordinate (D1) --++ (225:{2/2}) node [left] {$A_1$} coordinate (A1) -- cycle;\n        \\draw (A) ++ (2,2) node [right] {$B_1$} coordinate (B1) -- (B) (B1) --++ (45:{2/2}) (B1) --++ (-2,0);\n        \\draw [dashed] (A) --++ (45:{2/2}) node [left] {$D$} coordinate (D) --++ (2,0) (D) --++ (0,2);\n        \\draw [dashed] ($(A1)!0.3!(D1)$) node [above left] {$Q$} -- ($(B)!0.3!(A)$) node [below] {$P$};\n    \\end{tikzpicture}\n\\end{center}\n\\twoch{$[\\dfrac\\pi4,\\dfrac\\pi3]$}{$[\\arctan\\dfrac{\\sqrt{2}}2,\\arctan\\sqrt 2]$}{$[\\dfrac\\pi4,\\arctan\\sqrt 2]$}{$[\\arctan\\dfrac{\\sqrt{2}}2,\\dfrac\\pi2]$}",
         "objs": [
             "K0610004B"
         ],
@@ -105879,7 +105883,7 @@
             "第六单元"
         ],
         "genre": "选择题",
-        "ans": "",
+        "ans": "C",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -116412,7 +116416,7 @@
     },
     "004696": {
         "id": "004696",
-        "content": "如图, 在正方体$ABCD-A_1B_1C_1D_1$中, 点$MN$分别在棱$AA_1CC_1$上, 则``直线$MN\\perp\\text{直线}C_1B$''是``直线$MN\\perp\\text{平面}C_1BD$''的\\bracket{20}.\n\\begin{center}\n    \\begin{tikzpicture}\n        \\draw (0,0) node [below left] {$A$} coordinate (A) --++ (2,0) node [below right] {$B$} coordinate (B) --++ (40:{2/2}) node [right] {$C$} coordinate (C)\n        --++ (0,2) node [above right] {$C_1$} coordinate (C1)\n        --++ (-2,0) node [above left] {$D_1$} coordinate (D1) --++ (220:{2/2}) node [left] {$A_1$} coordinate (A1) -- cycle;\n        \\draw (A) ++ (2,2) node [right] {$B_1$} coordinate (B1) -- (B) (B1) --++ (40:{2/2}) (B1) --++ (-2,0);\n        \\draw [dashed] (A) --++ (40:{2/2}) node [left] {$D$} coordinate (D) --++ (2,0) (D) --++ (0,2);\n        \\draw ($(A)!0.8!(A1)$) node [left] {$M$} coordinate (M);\n        \\draw ($(C1)!0.8!(C)$) node [right] {$N$} coordinate (N);\n        \\draw [dashed] (M) -- (N)  (C1) -- (D) -- (B);\n        \\draw (B) -- (C1);\n    \\end{tikzpicture}\n\\end{center}\n\\twoch{充分非必要条件}{必要非充分条件}{充要条件}{既不充分又不必要条件}",
+        "content": "如图, 在正方体$ABCD-A_1B_1C_1D_1$中, 点$MN$分别在棱$AA_1CC_1$上, 则``直线$MN\\perp\\text{直线}C_1B$''是``直线$MN\\perp\\text{平面}C_1BD$''的\\bracket{20}.\n\\begin{center}\n    \\begin{tikzpicture}[scale = 0.6]\n        \\draw (0,0) node [below left] {$A$} coordinate (A) --++ (2,0) node [below right] {$B$} coordinate (B) --++ (40:{2/2}) node [right] {$C$} coordinate (C)\n        --++ (0,2) node [above right] {$C_1$} coordinate (C1)\n        --++ (-2,0) node [above left] {$D_1$} coordinate (D1) --++ (220:{2/2}) node [left] {$A_1$} coordinate (A1) -- cycle;\n        \\draw (A) ++ (2,2) node [right] {$B_1$} coordinate (B1) -- (B) (B1) --++ (40:{2/2}) (B1) --++ (-2,0);\n        \\draw [dashed] (A) --++ (40:{2/2}) node [left] {$D$} coordinate (D) --++ (2,0) (D) --++ (0,2);\n        \\draw ($(A)!0.8!(A1)$) node [left] {$M$} coordinate (M);\n        \\draw ($(C1)!0.8!(C)$) node [right] {$N$} coordinate (N);\n        \\draw [dashed] (M) -- (N)  (C1) -- (D) -- (B);\n        \\draw (B) -- (C1);\n    \\end{tikzpicture}\n\\end{center}\n\\twoch{充分非必要条件}{必要非充分条件}{充要条件}{既不充分又不必要条件}",
         "objs": [
             "K0609003B",
             "K0611002B"
@@ -116421,7 +116425,7 @@
             "第六单元"
         ],
         "genre": "选择题",
-        "ans": "",
+        "ans": "C",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -217016,7 +217020,7 @@
     },
     "009144": {
         "id": "009144",
-        "content": "如图, $EF$分别是空间四边形$ABCD$的边$BCAD$的中点, 过$EF$且平行于$AB$的平面与$AC$交于点$G$, 求证: $G$是$AC$的中点.\n\\begin{center}\n\\begin{tikzpicture}[>=latex]\n\\draw (0,0) node [left] {$B$} coordinate (B);\n\\draw (3,0) node [right] {$D$} coordinate (D);\n\\draw (2,-1) node [below] {$C$} coordinate (C);\n\\draw (1.5,2) node [above] {$A$} coordinate (A);\n\\draw ($(B)!0.5!(C)$) node [below left] {$E$} coordinate (E);\n\\draw ($(A)!0.5!(D)$) node [above right] {$F$} coordinate (F);\n\\draw ($(A)!0.5!(C)$) node [above left] {$G$} coordinate (G);\n\\draw (A) -- (B) -- (C) -- (D) -- cycle (A) -- (C) (E) -- (G) -- (F);\n\\draw [dashed] (E) -- (F) (B) -- (D);\n\\end{tikzpicture}\n\\end{center}",
+        "content": "如图, $E$、$F$分别是空间四边形$ABCD$的边$BC$、$AD$的中点, 过$EF$且平行于$AB$的平面与$AC$交于点$G$, 求证: $G$是$AC$的中点.\n\\begin{center}\n\\begin{tikzpicture}[>=latex]\n\\draw (0,0) node [left] {$B$} coordinate (B);\n\\draw (3,0) node [right] {$D$} coordinate (D);\n\\draw (2,-1) node [below] {$C$} coordinate (C);\n\\draw (1.5,2) node [above] {$A$} coordinate (A);\n\\draw ($(B)!0.5!(C)$) node [below left] {$E$} coordinate (E);\n\\draw ($(A)!0.5!(D)$) node [above right] {$F$} coordinate (F);\n\\draw ($(A)!0.5!(C)$) node [above left] {$G$} coordinate (G);\n\\draw (A) -- (B) -- (C) -- (D) -- cycle (A) -- (C) (E) -- (G) -- (F);\n\\draw [dashed] (E) -- (F) (B) -- (D);\n\\end{tikzpicture}\n\\end{center}",
         "objs": [
             "K0608004B"
         ],
@@ -217039,7 +217043,7 @@
     },
     "009145": {
         "id": "009145",
-        "content": "在长方体$ABCD-A_1B_1C_1D_1$中, 矩形$AA_1D_1D$和$D_1C_1CD$的中心分别为$MN$, 求证: $MN\\parallel$平面$ABCD$.\n\\begin{center}\n\\begin{tikzpicture}[>=latex]\n\\draw (0,0) node [below left] {$A$} coordinate (A) --++ (3,0) node [below right] {$B$} coordinate (B) --++ (45:{2/2}) node [right] {$C$} coordinate (C)\n--++ (0,2\n) node [above right] {$C_1$} coordinate (C1)\n--++ (-3,0) node [above left] {$D_1$} coordinate (D1) --++ (225:{2/2}) node [left] {$A_1$} coordinate (A1) -- cycle;\n\\draw (A) ++ (3,2\n) node [right] {$B_1$} coordinate (B1) -- (B) (B1) --++ (45:{2/2}) (B1) --++ (-3,0);\n\\draw [dashed] (A) --++ (45:{2/2}) node [left] {$D$} coordinate (D) --++ (3,0) (D) --++ (0,2\n);\n\\draw [dashed] ($(A)!0.5!(D1)$) node [above] {$M$} -- ($(C)!0.5!(D1)$) node [right] {$N$}; \n\\end{tikzpicture}\n\\end{center}",
+        "content": "在长方体$ABCD-A_1B_1C_1D_1$中, 矩形$AA_1D_1D$和$D_1C_1CD$的中心分别为$M$、$N$, 求证: $MN\\parallel$平面$ABCD$.\n\\begin{center}\n\\begin{tikzpicture}[>=latex]\n\\draw (0,0) node [below left] {$A$} coordinate (A) --++ (3,0) node [below right] {$B$} coordinate (B) --++ (45:{2/2}) node [right] {$C$} coordinate (C)\n--++ (0,2\n) node [above right] {$C_1$} coordinate (C1)\n--++ (-3,0) node [above left] {$D_1$} coordinate (D1) --++ (225:{2/2}) node [left] {$A_1$} coordinate (A1) -- cycle;\n\\draw (A) ++ (3,2\n) node [right] {$B_1$} coordinate (B1) -- (B) (B1) --++ (45:{2/2}) (B1) --++ (-3,0);\n\\draw [dashed] (A) --++ (45:{2/2}) node [left] {$D$} coordinate (D) --++ (3,0) (D) --++ (0,2\n);\n\\draw [dashed] ($(A)!0.5!(D1)$) node [above] {$M$} -- ($(C)!0.5!(D1)$) node [right] {$N$}; \n\\end{tikzpicture}\n\\end{center}",
         "objs": [
             "K0608004B"
         ],
@@ -217320,7 +217324,7 @@
     },
     "009158": {
         "id": "009158",
-        "content": "选择题:\n(1) $\\alpha,\\beta$是两个不重合的平面, $a,b$是两条不同的直线, 在下列条件中可判定$\\alpha \\parallel\\beta$的是\\bracket{20}.\n\\onech{平面$\\alpha,\\beta$都平行于直线$a,b$}{平面内有三个不共线的点到平面$\\beta$的距离相等}{$a,b$是平面$\\alpha$内的两条直线, 且$\\alpha \\parallel\\beta$, $b\\parallel\\beta$}{$a,b$是两条异面直线, 且$a\\parallel\\alpha$, $b\\parallel\\alpha$, $\\alpha \\parallel\\beta$, $b\\parallel\\beta$}",
+        "content": "$\\alpha,\\beta$是两个不重合的平面, $a,b$是两条不同的直线, 在下列条件中可判定$\\alpha \\parallel\\beta$的是\\bracket{20}.\n\\onech{平面$\\alpha,\\beta$都平行于直线$a,b$}{平面$\\alpha$内有三个不共线的点到平面$\\beta$的距离相等}{$a,b$是平面$\\alpha$内的两条直线, 且$a \\parallel\\beta$, $b\\parallel\\beta$}{$a,b$是两条异面直线, 且$a\\parallel\\alpha$, $b\\parallel\\alpha$, $a \\parallel\\beta$, $b\\parallel\\beta$}",
         "objs": [
             "K0612002B"
         ],
@@ -217467,7 +217471,9 @@
             "20220726\t王伟叶"
         ],
         "same": [],
-        "related": [],
+        "related": [
+            "030144"
+        ],
         "remark": "",
         "space": "12ex"
     },
@@ -228930,7 +228936,9 @@
             "20220730\t王伟叶"
         ],
         "same": [],
-        "related": [],
+        "related": [
+            "030149"
+        ],
         "remark": "",
         "space": "12ex"
     },
@@ -229023,7 +229031,7 @@
     },
     "009690": {
         "id": "009690",
-        "content": "如图, 已知$PA$垂直于平面$\\alpha$, $PB$垂直于平面$\\beta$, $A$、$B$为相应的垂足, 且$l$为平面$\\alpha$与平面$\\beta$的交线. 求证: $l\\perp$平面$PAB$.\n\\begin{center}\n\\begin{tikzpicture}[>=latex, scale = 1.5]\n\\draw (0,0,0) coordinate (O) (2,0,0) coordinate (R) (-1,1,0) coordinate (L);\n\\draw (O) ++ (0,0,2) coordinate (O1) (R) ++ (0,0,2) coordinate (R1) (L) ++ (0,0,2) coordinate (L1);\n\\draw (L) -- (L1) -- (O1) -- (R1) -- (R);\n\\path [name path = OR] (O) -- (R);\n\\path [name path = OL] (O) -- (L);\n\\draw [name path = AP] (1.5,0,1) node [right] {$A$} coordinate (A) --++ (0,2,0) node [right] {$P$} coordinate (P);\n\\draw [name path = BP] (A) --++ (-1.5,0,0) coordinate (O2) --++ (-0.7,0.7,0) node[above] {$B$} coordinate (B) -- (P);\n\\draw [name intersections = {of  = AP and OR, by = T}];\n\\draw [name intersections = {of  = BP and OL, by = S}];\n\\draw (O2) -- (O1) (T) -- (R) (S) -- (L);\n\\draw [dashed] (O) -- (O1) (T) -- (O) -- (S);\n\\draw (1.9,0,2) node [above] {$\\alpha$} (L1) ++ (0.2,-0.2,0) node [above] {$\\beta$} (O1) node [above] {$l$};\n\\end{tikzpicture}\n\\end{center}",
+        "content": "如图, 已知$PA$垂直于平面$\\alpha$, $PB$垂直于平面$\\beta$, $A$、$B$为相应的垂足, 且$l$为平面$\\alpha$与平面$\\beta$的交线. 求证: $l\\perp$平面$PAB$.\n\\begin{center}\n\\begin{tikzpicture}[>=latex, scale = 0.8]\n\\draw (0,0,0) coordinate (O) (2,0,0) coordinate (R) (-1,1,0) coordinate (L);\n\\draw (O) ++ (0,0,2) coordinate (O1) (R) ++ (0,0,2) coordinate (R1) (L) ++ (0,0,2) coordinate (L1);\n\\draw (L) -- (L1) -- (O1) -- (R1) -- (R);\n\\path [name path = OR] (O) -- (R);\n\\path [name path = OL] (O) -- (L);\n\\draw [name path = AP] (1.5,0,1) node [right] {$A$} coordinate (A) --++ (0,2,0) node [right] {$P$} coordinate (P);\n\\draw [name path = BP] (A) --++ (-1.5,0,0) coordinate (O2) --++ (-0.7,0.7,0) node[above] {$B$} coordinate (B) -- (P);\n\\draw [name intersections = {of  = AP and OR, by = T}];\n\\draw [name intersections = {of  = BP and OL, by = S}];\n\\draw (O2) -- (O1) (T) -- (R) (S) -- (L);\n\\draw [dashed] (O) -- (O1) (T) -- (O) -- (S);\n\\draw (1.9,0,2) node [above] {$\\alpha$} (L1) ++ (0.2,-0.2,0) node [above] {$\\beta$} (O1) node [above] {$l$};\n\\end{tikzpicture}\n\\end{center}",
         "objs": [
             "K0609003B"
         ],
@@ -229107,7 +229115,9 @@
             "20220730\t王伟叶"
         ],
         "same": [],
-        "related": [],
+        "related": [
+            "030143"
+        ],
         "remark": "",
         "space": "12ex"
     },
@@ -229183,7 +229193,7 @@
     },
     "009697": {
         "id": "009697",
-        "content": "判断下列命题的真假, 并说明理由:\\\\\n(1) 若一个平面内的两条直线均平行于另一个平面, 则这两个平面平行;\n(2) 若一个平面内两条不平行的直线都平行于另一个平面, 则这两个平面平行;\n(3) 若两个平面平行, 则其中一个平面中的任何直线都平行于另一个平面;\n(4) 平行于同一个平面的两个平面平行;\n(5) 若一个平面内的任何一条直线都平行于另一个平面, 则这两个平面平行.",
+        "content": "判断下列命题的真假, 并说明理由:\\\\\n(1) 若一个平面内的两条直线均平行于另一个平面, 则这两个平面平行;\\\\\n(2) 若一个平面内两条不平行的直线都平行于另一个平面, 则这两个平面平行;\\\\\n(3) 若两个平面平行, 则其中一个平面中的任何直线都平行于另一个平面;\\\\\n(4) 平行于同一个平面的两个平面平行;\\\\\n(5) 若一个平面内的任何一条直线都平行于另一个平面, 则这两个平面平行.",
         "objs": [
             "K0612002B",
             "K0612004B"
@@ -229201,7 +229211,9 @@
             "20220730\t王伟叶"
         ],
         "same": [],
-        "related": [],
+        "related": [
+            "030151"
+        ],
         "remark": "",
         "space": "12ex"
     },
@@ -229270,7 +229282,9 @@
             "20220730\t王伟叶"
         ],
         "same": [],
-        "related": [],
+        "related": [
+            "030150"
+        ],
         "remark": "",
         "space": "12ex"
     },
@@ -229293,7 +229307,9 @@
             "20220730\t王伟叶"
         ],
         "same": [],
-        "related": [],
+        "related": [
+            "030145"
+        ],
         "remark": "",
         "space": "12ex"
     },
@@ -288079,7 +288095,7 @@
         "same": [],
         "related": [],
         "remark": "",
-        "space": ""
+        "space": "18ex"
     },
     "030093": {
         "id": "030093",
@@ -288121,7 +288137,7 @@
         "same": [],
         "related": [],
         "remark": "",
-        "space": ""
+        "space": "18ex"
     },
     "030095": {
         "id": "030095",
@@ -288164,7 +288180,7 @@
         "same": [],
         "related": [],
         "remark": "",
-        "space": ""
+        "space": "18ex"
     },
     "030097": {
         "id": "030097",
@@ -288204,7 +288220,7 @@
         "same": [],
         "related": [],
         "remark": "",
-        "space": ""
+        "space": "18ex"
     },
     "030099": {
         "id": "030099",
@@ -288228,7 +288244,8 @@
         ],
         "same": [],
         "related": [
-            "009169"
+            "009169",
+            "030147"
         ],
         "remark": "",
         "space": "24ex"
@@ -289114,5 +289131,223 @@
         "related": [],
         "remark": "",
         "space": ""
+    },
+    "030143": {
+        "id": "030143",
+        "content": "如图, 平面$\\alpha$上的斜线$l$与平面$\\alpha$所成的角为$\\theta$, $l'$是$l$在平面$\\alpha$上的投影, $O$是$l$与平面$\\alpha$的交点, 点$B$是$l$上一点$A$在$\\alpha$上的投影, $OC$是$\\alpha$上的任意一条直线.\\\\\n(1) 如果$\\theta =45^\\circ$, $\\angle BOC=45^\\circ$, 求$\\angle AOC$;\\\\\n(2) 试证明:  $\\angle AOC>\\theta$.\n\\begin{center}\n\\begin{tikzpicture}[>=latex]\n\\draw (-1,0,0) -- (3,0,0) node [right] {$l'$} (2,2,0) node [above] {$A$} coordinate (A) -- (2,0,0) coordinate (B) node [below] {$B$} (2.5,2.5,0) node [right] {$l$} -- (0,0,0) coordinate (O) node [below] {$O$};\n\\draw (1,0,1) node [below] {$C$} coordinate (C);\n\\draw ($(O)!-0.5!(C)$) -- ($(O)!1.8!(C)$);\n\\draw [name path = edge] (-1.5,0,-2.5) coordinate (L) -- (-1.5,0,2.5) --++ (5,0,0) --++ (0,0,-5) coordinate (R);\n\\path [name path = LR] (L) -- (R);\n\\path [name path = OA] (O) -- (A);\n\\path [name path = AB] (A) -- (B);\n\\path [name intersections = {of = OA and LR, by = A1}];\n\\path [name intersections = {of = AB and LR, by = B1}];\n\\draw (L) -- (A1) (B1) -- (R);\n\\draw [dashed] (A1) -- (B1);\n\\path [name path = down] ($(O)!-0.6!(A)$) -- (O);\n\\path [name intersections = {of = down and edge, by = T}];\n\\draw (T) -- ($(O)!-0.6!(A)$);\n\\draw [dashed] (T) -- (O);\n\\draw (O) pic [\"$\\theta$\",draw,angle eccentricity = 1.5] {angle = B--O--A};\n\\draw (O) pic [scale = 1.1,draw,angle eccentricity = 1.7]{angle = C--O--B};\n\\end{tikzpicture}\n\\end{center}",
+        "objs": [],
+        "tags": [
+            "第六单元"
+        ],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "新教材必修第三册课堂练习-20221011修改",
+        "edit": [
+            "20220730\t王伟叶",
+            "20221011\t余利成"
+        ],
+        "same": [],
+        "related": [
+            "009693"
+        ],
+        "remark": "",
+        "space": "12ex"
+    },
+    "030144": {
+        "id": "030144",
+        "content": "已知不共面的三条射线$a,b,c$均以点$P$为端点, 平面$\\alpha,\\beta$与直线$a,b,c$分别相交于$A,B,C$和$A_1,B_1,C_1$, 且$\\dfrac{PA}{PA_1}=\\dfrac{PB}{PB_1}=\\dfrac{PC}{PC_1}$, 求证: $\\alpha \\parallel\\beta$.",
+        "objs": [],
+        "tags": [
+            "第六单元"
+        ],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "二期课改练习册高三-20221011修改",
+        "edit": [
+            "20220726\t王伟叶",
+            "20221011\t徐慧"
+        ],
+        "same": [],
+        "related": [
+            "009164"
+        ],
+        "remark": "",
+        "space": "12ex"
+    },
+    "030145": {
+        "id": "030145",
+        "content": "如图, 已知$AB\\perp$平面$BCD$, $BC\\perp CD$, 有哪些平面互相垂直? 选择其中一对互相垂直的平面给出证明. \n\\begin{center}\n\\begin{tikzpicture}[>=latex]\n\\draw (0,0,0) node [left] {$B$} coordinate (B) -- (2.4,0,1.6) node [below] {$C$} coordinate (C) -- (3.6,0,0) node [right] {$D$} coordinate (D) -- (0,2,0) node [above] {$A$} coordinate (A);\n\\draw (A) -- (B) (A) -- (C);\n\\draw [dashed] (B) -- (D); \n\\end{tikzpicture}\n\\end{center}",
+        "objs": [],
+        "tags": [
+            "第六单元"
+        ],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "新教材必修第三册课堂练习-20221011修改",
+        "edit": [
+            "20220730\t王伟叶",
+            "20221011\t徐慧"
+        ],
+        "same": [],
+        "related": [
+            "009701"
+        ],
+        "remark": "",
+        "space": "12ex"
+    },
+    "030146": {
+        "id": "030146",
+        "content": "过$60^\\circ$的二面角$\\alpha-l-\\beta$的棱上一点$A$, 分别在$\\alpha,\\beta$内引两条射线, 使得它们与$l$都成$45^\\circ$角, 则这两条射线夹角的余弦值为\\blank{60}.",
+        "objs": [],
+        "tags": [
+            "第六单元"
+        ],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2016届创新班作业\t2214-二面角[2]-20221011修改",
+        "edit": [
+            "20220625\t王伟叶",
+            "20221011\t徐慧"
+        ],
+        "same": [],
+        "related": [
+            "001665"
+        ],
+        "remark": "",
+        "space": ""
+    },
+    "030147": {
+        "id": "030147",
+        "content": "下列命题是否为真命题? 如果是, 请回答``真''; 如果不是, 请说明理由:\\\\\n(1) 垂直于同一直线的两个平面平行;\\\\\n(2) 平行于同一平面的两条直线平行;\\\\\n(3) 垂直于同一平面的两条直线平行.",
+        "objs": [],
+        "tags": [
+            "第六单元"
+        ],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "二期课改练习册高三-20221002修改-20221011修改",
+        "edit": [
+            "20220726\t王伟叶",
+            "20221002\t王伟叶",
+            "20221011\t吴惠群, 余利成"
+        ],
+        "same": [],
+        "related": [
+            "009169",
+            "030099"
+        ],
+        "remark": "",
+        "space": "24ex"
+    },
+    "030148": {
+        "id": "030148",
+        "content": "下列命题是否为真命题? 如果是, 请回答``真''; 如果不是, 请说明理由:\\\\\n(1) 若直线$l$与平面$M$斜交, 则$M$内不存在与$l$垂直的直线;\\\\\n(2) 若直线$l\\perp\\text{平面}M$, 则$M$内不存在与$l$不垂直的直线;\\\\\n(3) 若直线$l$与平面$M$斜交, 则$M$内不存在与$l$平行的直线;\\\\\n(4) 若直线$l\\parallel\\text{平面}M$, 则$M$内不存在与$l$不平行的直线.",
+        "objs": [],
+        "tags": [
+            "第六单元"
+        ],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "教材复习题-20221011修改",
+        "edit": [
+            "20220624\t王伟叶, 余利成",
+            "20221011\t吴惠群, 余利成"
+        ],
+        "same": [],
+        "related": [
+            "000178"
+        ],
+        "remark": "",
+        "space": "12ex"
+    },
+    "030149": {
+        "id": "030149",
+        "content": "下列命题是否为真命题? 如果是, 请回答``真''; 如果不是, 请说明理由:\\\\\n(1) 若两直线$a$、$b$互相平行, 则$a$平行于经过$b$的任何平面;\\\\\n(2) 若直线$a$与平面$\\alpha$平行, 则$a$平行于$\\alpha$内的任何直线;\\\\\n(3) 若两直线$a$、$b$都与平面$\\alpha$平行, 则$a\\parallel b$;\\\\\n(4) 若直线$a$平行于平面$\\alpha$, 直线$b$在平面$\\alpha$上, 则$a\\parallel b$或者$a$与$b$为异面直线.",
+        "objs": [],
+        "tags": [
+            "第六单元"
+        ],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "新教材必修第三册课堂练习-20221011修改",
+        "edit": [
+            "20220730\t王伟叶",
+            "20221011\t吴惠群, 余利成"
+        ],
+        "same": [],
+        "related": [
+            "009685"
+        ],
+        "remark": "",
+        "space": "12ex"
+    },
+    "030150": {
+        "id": "030150",
+        "content": "已知平面$\\alpha\\perp$平面$\\beta$, 下列命题是否为真命题? 如果是, 请回答``真''; 如果不是, 请说明理由:\\\\ \n(1) 平面$\\alpha$上的任意一条直线都垂直于平面$\\beta$上的任意一条直线;\\\\\n(2) 平面$\\alpha$上的任意一条直线都垂直于平面$\\beta$上的无数条直线;\\\\\n(3) 平面$\\alpha$上的任意一条直线都垂直于平面$\\beta$;\\\\\n(4) 过平面$\\alpha$上任意一点作平面$\\alpha$与$\\beta$交线的垂线$l$, 则$l\\perp \\beta$.",
+        "objs": [],
+        "tags": [
+            "第六单元"
+        ],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "新教材必修第三册课堂练习-20221011修改",
+        "edit": [
+            "20220730\t王伟叶",
+            "20221011\t吴惠群, 徐慧"
+        ],
+        "same": [],
+        "related": [
+            "009700"
+        ],
+        "remark": "",
+        "space": "12ex"
+    },
+    "030151": {
+        "id": "030151",
+        "content": "下列命题是否为真命题? 如果是, 请回答``真''; 如果不是, 请说明理由:\\\\\n(1) 若一个平面内的两条直线均平行于另一个平面, 则这两个平面平行;\\\\\n(2) 若一个平面内两条不平行的直线都平行于另一个平面, 则这两个平面平行;\\\\\n(3) 若两个平面平行, 则其中一个平面中的任何直线都平行于另一个平面;\\\\\n(4) 平行于同一个平面的两个平面平行;\\\\\n(5) 若一个平面内的任何一条直线都平行于另一个平面, 则这两个平面平行.",
+        "objs": [],
+        "tags": [
+            "第六单元"
+        ],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "新教材必修第三册课堂练习-20221011修改",
+        "edit": [
+            "20220730\t王伟叶",
+            "20221011\t吴惠群, 徐慧"
+        ],
+        "same": [],
+        "related": [
+            "009697"
+        ],
+        "remark": "",
+        "space": "12ex"
     }
 }
\ No newline at end of file