Fork me on GitHub

2014全国甲&2015福建-几何题

 1 ---
 2 > id: xie01
 3 
 4 ### 2014 国标甲
 5 
 6 ::: column.grow
 7 
 8 如图所示四棱柱 P-ABCD 中,四边形 ABCD 是矩形,底面 ABCD 为矩形,PA ⊥ 平面 ABCD, E 为 PD  的中点.
 9 
10 求证:_{.b.m-red}PB_ ∥ _{.m-blue}平面 AEC_.
11 
12 ::: column(width=480)
13 
14     figure
15       x-geopad(width=480 height=400 x-axis="-0.6,1.8,.1" y-axis="-0.8,1.2,.1"   padding=5): svg
16         circle.blue(x="bimetric(0,0,0)" name="a" label="A")
17         circle.red(x="bimetric(1.5,0,0)" name="b" label="B")
18         circle.blue(x="bimetric(1.5,1.73,0)" name="c" label="C")
19         circle(x="bimetric(0,1.73,0)" name="d" label="D")
20         circle.blue(x="bimetric(0,1.73/2,0.5)" name="e" label="E")
21         circle.red(x="bimetric(0,0,1)" name="p" label="P")
22         path(x="polygon(p,b,c,d)")
23         path(x="polygon(p,c,e)")
24         path(x="segment(a,p)" style = "stroke-dasharray: 8px 10px")
25         path(x="segment(a,b)" style = "stroke-dasharray: 8px 10px")
26         path.blue(x="segment(a,c)" style = "stroke-dasharray: 8px 10px")
27         path(x="segment(a,d)" style = "stroke-dasharray: 8px 10px")
28         path.blue(x="segment(a,e)" style = "stroke-dasharray: 8px 10px")
29         path(x="segment(b,d)" style = "stroke-dasharray: 8px 10px")
30         path.red(x="segment(p,b)" )
31         path.fill.blue.light(x="polygon(a,e,c)")
32         path.blue(x="segment(e,c)" )
33 
34 :::
35 
36 ---
37 > id: xie02
38 
39 ### 2015 福建
40 
41 ::: column.grow
42 
43 如图所示,在几何体ABCDE中,四边形ABCD是矩形, AB ⊥  平面BEC,BE ⊥ EC,AB=BE=EC=2,G,F分别是线段的BE,DC的中点.
44 
45 求证:_{.b.m-red}GF_ ∥ _{.m-blue}平面 ADE_.
46 
47 ::: column(width=460)
48 
49     figure
50       x-geopad(width=460 height=480 x-axis="-0.8,1.6,0.2" y-axis="-0.8,1.6,0.2"  padding=5): svg
51         circle.blue(x="bimetric(0,0,1.6)" name="a" label="A")
52         circle(x="bimetric(0,0,0)" name="b" label="B")
53         circle(x="bimetric(2,2,0)" name="c" label="C")
54         circle.blue(x="bimetric(2,2,1.6)" name="d" label="D")
55         circle.blue(x="bimetric(2,0,0)" name="e" label="E")
56         circle.red(x="bimetric(2,2,0.8)" name="f" label="F")
57         circle.red(x="bimetric(1,0,0)" name="g" label="G")
58         path(x="polygon(a,e,c,d)")
59         path(x="polygon(d,e,f)")
60         path(x="segment(b,a)" style = "stroke-dasharray: 8px 10px")
61         path(x="segment(b,e)" style = "stroke-dasharray: 8px 10px")
62         path(x="segment(b,c)" style = "stroke-dasharray: 8px 10px")
63         path(x="segment(f,a)" style = "stroke-dasharray: 8px 10px")
64         path.red(x="segment(f,g)" style = "stroke-dasharray: 8px 10px")
65         path.fill.blue.light(x="polygon(a,d,e)")
66         path.blue(x="segment(e,a)" )
67         path.blue(x="segment(d,a)" )
68         path.blue(x="segment(e,d)" )
69 
70 :::
content.md

 

 

 

posted @ 2020-03-06 22:21  小奔奔  阅读(153)  评论(0编辑  收藏  举报