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§4-4 点线面综合题举例. 画法几何问题,归纳起来大体分为 定位问题 和 度量问题 两大类。. ( 1 ) 题意分析. 分析有哪些几何条件,有无几何元素在空间处于特殊位置,明确求解的几何元素或几何量。. ( 2 ) 空间分析. 轨迹分析法 逆推法. ( 3 ) 投影作图. ( 4 ) 解答分析. B. b’. C. k’. e’. c’. s’. K. f’. A. F. a’. c. S. f. s. a. E. e. b. k.

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§4-4 点线面综合题举例

画法几何问题,归纳起来大体分为定位问题和度量问题两大类。

(1) 题意分析

分析有哪些几何条件,有无几何元素在空间处于特殊位置,明确求解的几何元素或几何量。

(2) 空间分析

轨迹分析法 逆推法

(3) 投影作图

(4) 解答分析


B

b’

C

k’

e’

c’

s’

K

f’

A

F

a’

c

S

f

s

a

E

e

b

k

例题1过点K作直线KS平行于三角形ABC并与直线EF相交。

(1) 过K作平面平行三角形ABC

(2) 求出EF与辅助平面的交点S

(3) 连KS即为所求


B

b’

C

k’

e’

M

c’

K

F

f’

A

a’

c

S

N

E

f

a

e

b

k

例题1 过点K作直线KS平行于三角形ABC并与直线EF相交。


b’

d’

a’

c’

b

d

a

c

例题2:求交叉两直线AB和CD的公垂线MN。


b’

A

d’

A

B

N

a’

C

c’

E

N

K

b

M

D

B

d

M

D

C

b

n

a

c( d )

a

c

分 析

m


n’

m’

b’

X

m2

(d2 )

n

c2

a2

d’

d1’

n2

m

a’

b2

c’

c1’

b

d

b1’

a1’

X1

X2

a

c

m1’

n1’


C

B

D

A

θ

例题3:求三角形ABC及BCD两平面之间的夹角。

b’

c’

d’

a’

X

a

c

d

b


b’

c’

a1’

d’

a’

X

a

c

θ

c1’( b1’)

d1’

d

b

X1


b’

a’

c’

d’

X

b

a

c

b1’(a1’)

d

c1’

(d1’)

X2

例题4以DC为直角边作等腰直角△CDE(∠CDE=90)且与ABCD平面垂直。

e1’


V

b’

b’

B

a’

a’

c’

X

C

A

H

b

a

例题5:已知等边三角形ABC , 点C在H面上 , 求此三角形的两面投影。


c’

b

a

c

b’

1. 求边AB的实长

2. 求边AC的水平投影

a’

3. 求边BC的水平投影

4. 求c , c’并连线

X

b

a


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