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anfal bel
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anfal bel
03-07-2015


ﻣﻨﺎﻗﺔﺸ ) 1 ( ) 2 ( ) 3 ( ) 4 ( ﻣﻦ ﺧﺘﺒﺮ ﻣﻜﺘﺴﺒﺎﻚﺗ
) 1 ( ﻧﺸﺎ ﻣﺘﻮ ﻷﺿﻼ ABCD
ﺧﺮ ﻟﻤﺴﺘﻘﯿﻤﺎ ﻟﻤﺘﻮﯾﺔ ﻟﻘﻄﻊ ﻟﻤﺘﻘﺎﯾﺴﺔ ﻣﻦ ﻟﺸﻜﻞ
) 2 ( ﯾﻮﺪﺟ 7 ﻣﺘﻮﯾﺎ ﺿﻼ
) 3 ( ﯾﻮﺟﺪ ﺑﻊ ﻣﺘﻮﯾﺎ ﺿﻼ ﺳﮭﺎ ﻟﻨﻘﻂ
D , C , B , A
) 4 ( ﻧﻘﻞ ﻟﺸﻜﻞ ﻧﺸﺎ ﻣﺘﻮ ﻷﺿﻼ ABFG
AKBG
ﻧﺸﺎ ) 1 ( 172
) ﻟﻌﻤﻞ ﯾﻜﻮ ﻋﻠﻰ ﻗﺔ ﻣﺮﺻﻮﻓﺔ ﺗﺤﻀﺮ ﻓﻲ ﻟﺒﯿﺖ (
ﻟﻤﻄﻠﻮ ﻣﻦ ﻟﺘﻼﻣﯿﺬ ﯾﺸﺮﺣﻮ ﻟﺰﻣﻼﺋﮭﻢ ﻛﯿﻒ ﻧﺠﺰ ﻟﻌﻤﻞ
* ﺳﺘﻌﻤﺎ ﻣﺮﺑﻌﺎ ﻟﻤﺮﺻﻮﻓﺔ ﯾﺴﺎﻋﺪ ﻋﻠﻰ ﻧﺠﺎ ﻟﻌﻤﻞ ﯾﻜﻮ ﻟﻚ ﺑﺈﻋﺘﺒﺎ ﻗﻄﻊ ﻟﺸﻜﻞ ﻛﺄﺿﻼ ﻗﻄﺎ ﻟﻤﺘﻮﯾﺎ
ﺿﻼ ﯾﺠﺪϪﺎ ﻟﺘﻠﻤﯿﺬ ﻋﺘﺒﺎ ﻃﻮ ﻟﻤﺮﺑﻊ ﻟﺼﻐﯿﺮ ﻟﺬ ﺗﺘﺸﻜﻞ ﻣﻨﮫ ﻟﻤﺮﺻﻮﻓﺔ ﻛﻮﺣﺪ ﻟﻸﻃﻮ .
ﻧﺸﺎ ) 2 ( 172
ﻟﻌﻤﻞ ﯾﻜﻮ ﻋﻠﻰ ﻗﺔ ﺮﻣ ﺻﻮﺔﻓ
ﺳﻢ ﻟﺸﻜﻞ ﻋﻠﻰ ﻗﺔ ﻣﺮﺻﻮﻓﺔ ﺣﯿﺚ ﺗﻮﺿﻊ ﻟﻨﻘﻂ C , B , A ﻛﻞ ﻟﻨﻘﻂ ﻷﺧﺮ ﻋﻠﻰ ﻣﺮﺑﻌﺎ ﻟﻤﺮﺻﻮﺔﻓ
1 ( ﻟﺮﺑﺎﻋﻲ ABB'A' ﻣﺘﻮ ﺿﻼ ﻣﻨﮫ ﻟﺮﺑﺎﻋﻲ AA'B'B ﻣﺘﻮ ﺿﻼ
ﻟﺮﺑﺎﻋﻲ BCC'B' ﻣﺘﻮ ﺿﻼ ﻣﻨﮫ ﻟﺮﺑﺎﻋﻲ AA'C'C ﻣﺘﻮ ﺿﻼ
ﻟﺮﺑﺎﻋﻲ CDD'C' ﻣﺘﻮ ﺿﻼ ﻣﻨﮫ ﻟﺮﺑﺎﻋﻲ
AA'D'D ﻣﺘﻮ ﺿﻼ
ﻟﺮﺑﺎﻋﻲ DEE'D' ﻣﺘﻮ ﺿﻼ ﻣﻨﮫ ﻟﺮﺑﺎﻋﻲ
ﺣﻠﻮﻝ ﲤﺎﺭﻳﻦ ﺍﻟﻜﺘﺎﺏ ﺍﳌﺪﺭﺳﻲ ﺍﻟﺴﻨﺔ ﺍﻟﺜﺎﻟﺜﺔ ﻣﺘﻮﺳﻂ ﺩﺍﺭ ﻧﺰﻫﺔ ﺍﻷﻟﺒﺏﺎ

3
AA'E'E ﻣﺘﻮ ﺿﻼ
2 ( ﻟﻨﻘﺔﻄ B ﻟﯿﺴﺖ ﺻﻮ ﻟﻨﻘﺔﻄ B' ﺑﺎﻹﻧﺴﺤﺎ ﻟﺬ ﯾﺤ ﻮ A ﻟﻰ A'
ﻟﻨﻘﺔﻄ C ﻟﯿﺴﺖ ﺻﻮ B ﺑﺎﻹﻧﺴﺤﺎ ﻟﻤﺬﻛﻮ ﻷ ﻟﺮﺑﺎﻋﻲ CBA'A ﻟﯿﺲ ﻣﺘﻮ ﺿﻼ
) ﻟﻘﻄﺔﻌ ] CB [ ﻻﺗﻮ ﻟﻘﻄﺔﻌ ] AA' ( [
J ﻟﯿﺴﺖ ﺻﻮ I ﺑﺎﻹﻧﺴﺤﺎ ﻟﻤﺬﻛﻮ ﻷ ﻟﺮﺑﺎﻋﻲ JIA'A ﻟﯿﺲ ﻣﺘﻮ ﺿﻼ ) ﻟﻘﻄﺔﻌ ] CB [ ﻻ ﺗﻘﺎﯾﺲ ﻟﻘﻄﺔﻌ ] AA' [
3 ( ﺑﺎﻹﻧﺴﺤﺎ ﻟﺬ ﯾﺤ ﻮ A ﻟﻰ A' B' ﻲ ﺻﻮ B C' ﻲ ﺻﻮ C D' ﻲ ﺻﻮ D
4 ( B' ﻲ ﺻﻮ B ﺑﺎﻹﻧﺴﺤﺎ ﻟﺬ ﯾﺤ ﻮ A ﻟﻰ A' ﻓﺈ ﻟﺮﺑﺎﻋﻲ ABB'A' ﻣﺘﻮ ﺿﻼ ﻋﻠﯿﮫ
) AB ) // ( A'B' (
BC = B'C' ﻷ ﻟﺮﺑﺎﻋﻲ BCC'B' ﻣﺘﻮ ﺿﻼ
5 ( ) AE // ( (A'E') ) BE ( ) // B'E' (
BD = B'D' AC = A'C'
C B A = ' '

' C B A C D E = ' '

' C D E
ﺣﻞ ﻧﺸﺎ ) 5 ( ﻦﻣ ﺧﺘﺒﺮ ﻣﻜﺘﺴﺒﺎﻚﺗ
1 ( AB +BC < AC AB + AC < BC
BI + CI = BC
2 ( ﻛﺎ AD +DB = AB ﯾﻜﻮ ﻣﻮﻊﻗ D ﻋﻠﻰ ﻟﻘﻄﺔﻌ ] AB [
ﻧﺸﺎ ) 3 ( 173
ﺬ ﻟﻨﺸﺎ ﯾﻜﻮ ﻣﺤﻀﺮ ﻓﻲ ﻟﺒﯿﺖ ﻋﻠﻰ ﻗﺔ ﻣﻠﯿﻤﺘﺮﺔﯾ
ﻟﻤﻄﻠﻮ ﻣﻦ ﻟﺘﻼﻣﯿﺬ ﺷﺮ ﻛﯿﻔﯿﺔ ﻋﻤﻠﯿﺔ ﻟﺘﺒﻠﯿﻂ ﻟﺘﻲ ﺗﻤﺖ ﻋﻠﻰ ﻟﻮﻗﺔ ﻟﻤﻠﯿﻤﺘﺮﺔﯾ
ﻟﺒﻼﺔﻃ 2 ﻲ ﺻﻮ ﻟﺒﻼﺔﻃ 1 ﺑﺎﻹﻧﺴﺤﺎ ﻟﺬ ﯾﺤﻮ A ﻟﻰ B
ﺣﻠﻮﻝ ﲤﺎﺭﻳﻦ ﺍﻟﻜﺘﺎﺏ ﺍﳌﺪﺭﺳﻲ ﺍﻟﺴﻨﺔ ﺍﻟﺜﺎﻟﺜﺔ ﻣﺘﻮﺳﻂ ﺩﺍﺭ ﻧﺰﻫﺔ ﺍﻷﻟﺒﺏﺎ

4
ﺑﺎﻹﻧﺴﺤﺎ ﻟﺬ ﯾﺤﻮ C ﻟﻰ D ﻟﺒﻼﺔﻃ 4 ﻲ ﺻﻮ ﻟﺒﻼﺔﻃ 3
ﻧﺸﺎ ) 4 ( 173
1 ( ﻧﻘﻞ ﻟﻘﻄﺔﻌ ] AB [ ﻟﻨﻘﻄﺘﯿﻦ C D ﻋﻠﻰ ﻗﺔ ﺑﯿﻀﺎ
2 ( M ﻧﻘﻄﺔ ﻛﯿﻔﯿﺔ ﻦﻣ ] AB [
ﻧﺸﺎ ﻟﻨﻘﻂ A' B' M' ﻮﺻ A B M ﻋﻠﻰ ﻟﺘﺮﺗﯿﺐ ﺑﺎﻹﻧﺴﺤﺎ ﻟﺬ ﯾﺤﻮ D ﻟﻰ C
ﺻﻮ ﻟﻘﻄﺔﻌ ] AB [ ﺑﺎﻹﻧﺴﺤﺎ ﻟﺬ ﯾﺤﻮ D ﻟﻰ C ﻲ ﻟﻘﻄﺔﻌ ] A'B' [
ﻧﺸﺎ ) 5 ( 173
1 ( ﻧﻘﻞ ﻟﻤﺴﺘﻘﻢﯿ ) d ( ﻟﻨﻘﻄﺘﻦﯿ A B ﻋﻠﻰ ﻗﺔ ﺑﯿﻀﺎ
2 ( M N ﻧﻘﻄﺘﺎ ﻣﺨﺘﻠﻔﺘﺎ ﻦﻣ ) d (
3 ( ﻧﺸﺎ ﻟﻨﻘﻄﺘﻦﯿ M' N' ﺻﻮﺗﻲ M N ﻋﻠﻰ ﻟﺘﺮﺗﯿﺐ ﺑﺎﻹﻧﺴﺤﺎ ﻟﺬ ﯾﺤﻮ A ﻟﻰ B
ﺛﻢ ﺳﻢ ﻟﻤﺴﺘﻘﻢﯿ ) M'N' (
ﻃﺒﯿﻌﺔ ﻟﺮﺑﺎﻋﻲ MNN'M' ﻣﺘﻮ ﺿﻼ
ﻟﻤﺴﺘﻘﯿﻤﻦﯿ ) d ( ) M'N' ( ﻣﺘﻮﯾﺎ
ﺻﻮ ﻟﻤﺴﺘﻘﻢﯿ ) d ( ﺑﺎﻹﻧﺴﺤﺎ ﻟﺬ ﯾﺤﻮ A ﻟﻰ B ﻮ ﻟﻤﺴﺘﻘﻢﯿ ) M'N' (

ﻣﻨﺎﻗﺸﺔ ﺗﻤﺮﯾﻦ 11 182
ﺻﻮ ) AB ( ﺑﺎﻹﻧﺴﺤﺎ ﻟﺬ ﯾﺤﻮ E ﻟﻰ F ﻮ ) HF (
ﺻﻮ ﻟﻤﺜﺚﻠ HAE ﺑﺎﻹﻧﺴﺤﺎ ﻟﺬ ﯾﺤ ﻮ A ﻟﻰ O ﻮ ﻟﻤﺜﺚﻠ GOF
ﻧﺸﺎ ) 6 ( 174
1 ( ﻧﻘﻞ ﻧﺼﻒ ﻟﻤﺴﺘﻘﻢﯿ ) OX [ ﻟﻨﻘﻄﺘﯿﻦ A B ﻋﻠﻰ ﻗﺔ ﺑﯿﻀﺎ
ﺣﻠﻮﻝ ﲤﺎﺭﻳﻦ ﺍﻟﻜﺘﺎﺏ ﺍﳌﺪﺭﺳﻲ ﺍﻟﺴﻨﺔ ﺍﻟﺜﺎﻟﺜﺔ ﻣﺘﻮﺳﻂ ﺩﺍﺭ ﻧﺰﻫﺔ ﺍﻷﻟﺒﺏﺎ

5
ﺧﺬ ﻧﻘﺔﻄ M ﻦﻣ ) OX [
ﻧﺸﺎ O' M' ﺻﻮﺗﻲ O M ﺑﺎﻹﻧﺴﺤﺎ ﻟﺬ ﯾﺤ ﻮ A ﻟﻰ B
ﺻﻮ ) OX [ ﺑﺎﻹﻧﺴﺤﺎ ﻟﺬ ﯾﺤﻮ A ﻟﻰ B ﻮ ﻧﺼﻒ ﻟﻤﺴﺘﻘﻢﯿ ) O'M' [ ﻟﺬ ﯾﻮﯾﮫ ﻟﮫ ﻣﻌﮫ ﻧﻔﺲ ﻹﺗﺠﺎ
ﻧﺸﺎ ) 7 ( 174
ﻧﻘﻞ ﻟﺸﻜﻞ ﻋﻠﻰ ﻗﺔ ﺑﯿﻀﺎ
M ﻧﻘﻄﺔ ﻣﻦ ﻟﺪﺋﺮ ) C (
ﻧﺸﺎ O' M' ﺻﻮﺗﻲ O M ﻋﻠﻰ ﻟﺘﺮﺗﯿﺐ ﺑﺎﻹﻧﺴﺤﺎ ﻟﺬ ﯾﺤ ﻮ A ﻟﻰ B
ﻃﺒﯿﻌﺔ ﻟﺮﺑﺎﻋﻲ OMM'O' ﻣﺘﻮ ﺿﻼ
ﻟﻄﻮ O'M' ﻮ ﻧﺼﻒ ﻗﻄﺮ ﻟﺪﺋﺮ ) C' ( ﻟﺘﻲ ﻣﺮﻛﺰﺎ O'
ﻣﻮﻗﻊ ﻟﻨﻘﺔﻄ M' ﻲ ﻧﻘﻄﺔ ﻣﻦ ﻟﺪﺋﺮ ) C' (
ﺻﻮ ﻟﺪﺋﺮ ) C ( ﺑﺎﻹﻧﺴﺤﺎ ﻟﺬ ﯾﺤ ﻮ A ﻟﻰ B ﻮ ﻟﺪﺋﺮ ) C' (

ﻧﺸﺎ ) 1 ( 177
ﯾﻜﻮ ﺬ ﻟﻨﺸﺎ ﻣﺤﻀﺮ ﻓﻲ ﻟﺒﯿﺖ ﻋﻠﻰ ﻗﺔ ﻣﺮﺻﻮﻓﺔ ﻣﻊ ﺿﺮ ﺣﻀﺎ ﻗﺔ ﺷﻔﺎﻓﺔ ﻣﺮﺳﻮ ﻋﻠﯿﮭﺎ ﻟﺴﯿﺎ
ﻣ ﻼﺣﺔﻈ : ﻟﺴﯿﺎ ﻗﺎﺑﻠﺔ ﻟﻠﺘﻄﺎﺑﻖ ﻣﻊ ﺻﻮﺗﺎﮭ
ﻧﺸﺎ ) 2 ( 177
1 ( ﺳﻢ ﻟﺸﻜﻞ ﻋﻠﻰ ﻗﺔ ﺑﯿﻀﺎ ﻋﻠﻰ ﻛﺮ ﻷﻧﺸﺔﻄ
2 ( ﻧﺸﺎ B' C' ﺻﻮﺗﻲ B C ﻋﻠﻰ ﻟﺘﺮﺗﯿﺐ ﺑﺎﻹﻧﺴﺤﺎ ﻟﺬ ﯾﺤ ﻮ A ﻟﻰ I
ﺣﻠﻮﻝ ﲤﺎﺭﻳﻦ ﺍﻟﻜﺘﺎﺏ ﺍﳌﺪﺭﺳﻲ ﺍﻟﺴﻨﺔ ﺍﻟﺜﺎﻟﺜﺔ ﻣﺘﻮﺳﻂ ﺩﺍﺭ ﻧﺰﻫﺔ ﺍﻷﻟﺒﺏﺎ

6
ﺻﻮ ﻟﻤﺜﺚﻠ ABC ﺑﺎﻹﻧﺴﺤﺎ ﻟﺬ ﯾﺤ ﻮ A ﻟﻰ I ﻮ ﻟﻤﺜﺚﻠ IB' C'
ﻃﺒﯿﻌﺔ ﻟﻤﺜﺚﻠ IB'C' ﻮ ﻣﺜﻠﺚ ﻣﺘﻘﺎﯾﺲ ﻷﻼﺿ ﻮ ﯾﻘﺎﯾﺲ ﻟﻤﺜﺚﻠ ABC ﻓﺈ ﻟﻤﺴﺎﺣﺘﯿﻦ ﻣﺘﺴﺎﯾﺘﺎ
3 ( ﻣﻮﻊﻗ I' ﺻﻮ I ﺑﻮﺳﻄﺔ ﺬ ﻹﻧﺴﺤﺎ ﻮ ﻣﻨﺘﺼﻒ ] C'B' [ ﻷ I ﻣﻨﺘﺼﻒ ] CB [ ﺻﻮ ] CB [ ﺑﻮﺳﻄﺔ ﺬ ﻹﻧﺴﺤﺎ
ﻮ ] C'B' [
ﻧﺸﺎ J' K' ﺻﻮﺗﻲ J K ﻋﻠﻰ ﻟﺘﺮﺗﯿﺐ ﺑﺎﻹﻧﺴﺤﺎ ﻟﻤﻌﻰﻄ
4 ( ﺻﻮ ﻟﻤﺴﺘ ﻘﯿﻢ ) JK ( ﺑﺎﻹﻧﺴﺤﺎ ﻟﻤﻌﻄﻰ ﻮ ) J'K' ( ﻷ ﻟﺪﯾﻨﺎ ﺻﻮ ] AB [ ﺑﻮﺳﻄﺔ ﺬ ﻹﻧﺴﺤﺎ ﻮ ] IB' [ J
ﻣﻨﺘﺼﻒ ] AB [
ﻟﺪﯾﻨﺎ ﯾﺎﻀ J' ﺻﻮ J ﺑﮭﺬ ﻹﻧﺴﺤﺎ ﺬ ﯾﻌﻨﻲ J' ﻣﻨﺘﺼﻒ ] IB' [
ﺑﻨﻔﺲ ﻟﻄﺮﯾﻘﺔ ﻧﺒﺮﻦ K' ﻣﻨﺘﺼﻒ ] IC' [
ﺣﺴﺐ ﻧﻈﺮﯾﺔ ﻣﺴﺘﻘﯿﻢ ﻟﻤﻨﺘﺼﻔﯿﻦ ﻓﺈ ) J'K' )//( B'C' (
5 ( ﺑﺎﻹﻧﺴﺤﺎ ﻟﺬ ﯾﺤ ﻮ A ﻟﻰ I :
ﺻﻮ ﻟﻤﺜﺚﻠ ABC ﻲ ﻟﻤﺜﺚﻠ IB'C' ﺻﻮ ﻛﻞ ﻗﻄﻌﺔ ﻣﺴﺘﻘﯿﻢ ﺑﻮﺳﻄﺔ ﻧﺴﺤﺎ ﻲ ﻗﻄﻌﺔ ﻣﺴﺘﻘﻢﯿ ﺗﻘﺎﯾﺴﮭﺎ ﻟﻤﺜﻠﺜﺎ
ABC IB'C' ﻤﺎ ﻣﺜﻠﺜﺎ ﻣﺘﻘﺎﯾﺴﺎ ﺑﺎﻟﺘﺎﻟﻲ ﻟﮭﻤﺎ ﻧﻔﺲ ﻟﻤﺴﺎﺣﺔ
ﻟﻨﻘﺔﻄ I' ﻲ ﻣﻨﺘﺼﻒ ﻟﻀﻠﻊ ] B'C' [ ﻷﻧﮭﺎ ﺻﻮ ﻟﻨﻘﺔﻄ I ﻣﻨﺘﺼﻒ ﻟ ﻀﻠﻊ ] BC [
ﻟﻨﻘﻄﺘﻦﯿ J' K' ﻤﺎ ﻣﻨﺘﺼﺎﻔ ﻟﻀﻠﻌﯿﻦ ] IB' [ ] IC' [ ﻋﻠﻰ ﻟﺘﺮﺗﯿﺐ ﻷﻧﮭﻤﺎ ﺻﻮﺗﺎ ﻟﻨﻘﻄﺘﻦﯿ J K ﻣﻨﺘﺼﻔﺎ ﻟﻀﻠﻌﯿﻦ ] AB [

] AC [ ﻋﻠﻰ ﻟﺘﺮﺗﯿﺐ
ﺻﻮ ﻟﻤﺴﺘﻘﻢﯿ ) JK ( ﻲ ) J'K' ( ﻷ ﺻﻮ ﻣﺴﺘﻘﯿﻢ ﺑﺈﻧﺴﺤﺎ ﻲ ﻣﺴﺘﻘﻢﯿ ﺬ ﻟﻤﺴﺘﻘﯿﻤﺎ ﻣﺘﻮﯾﺎ
ﻟﻤﺴﺘﻘﻢﯿ ) J'K' ( ) B'C' ( ﻣﺘﻮ ﯾﺎ ﻷ :
) B'C' ( // ) BC ( ﻷ ) B'C' ( ﻮ ﺻﻮ ﻟﻤﺴﺘﻘﻢﯿ ) BC ( ﺑﺈﻧﺴﺤﺎ
) JK ( // ) BC ( ﻷ ) JK ( ﻮ ﻣﺴﺘﻘﻢﯿ ﻟﻤﻨﺘﺼﻔﯿﻦ ﻓﻲ ﻟﻤﺜﺚﻠ ABC
) JK ( ) // B'C' ( ﻋﻠﻤﺎ ) J'K' ( // ) JK (
ﻓﺈ ) J'K' ( ﯾﻮ ) B'C' (
ﺣﻞ ﺗﻤﺮﯾﻦ 12 183
ﺻﻮﺗﻲ M A ﺑﺎﻹﻧﺴﺤﺎ ﻟﺬ ﯾﺤ ﻮ T ﻟﻰ A
ﺣﻠﻮﻝ ﲤﺎﺭﻳﻦ ﺍﻟﻜﺘﺎﺏ ﺍﳌﺪﺭﺳﻲ ﺍﻟﺴﻨﺔ ﺍﻟﺜﺎﻟﺜﺔ ﻣﺘﻮﺳﻂ ﺩﺍﺭ ﻧﺰﻫﺔ ﺍﻷﻟﺒﺏﺎ

7
1 ( ﺻﻮ M ﻲ P ) ﻷ M ﻲ ﻣﻨﺘﺼﻒ ] TP [ ) TM ) // ( MP ( MP = TM (
ﺻﻮ A ﻲ R ) ﻷ ﻟﺮﺑﺎﻋﻲ TMRA ﻣﺘﻮ ﺿﻼ (
2 ( ﺻﻮ ] AM [ ﺑﺎﻹﻧﺴﺤﺎ ﻟﺬ ﯾﺤ ﻮ T ﻟﻰ A ﻲ ] SR [ ﻷ ﻟﺮﺑﺎﻋﻲ ASRM ﻣﺘﻮ ﺿﻼ ﺬ ﻷ A ﻣﻨﺘﺼﻒ
] TS [
) TA )// ( AS ( AS = TA
ﺻﻮ M ﻲ R ﺑﻮﺳﻄﺔ ﺬ ﻹﻧﺴﺤﺎ
) MR ) // ( AS ( AS = MR
ﺣﻞ ﺗﻤﺮﯾﻦ 14 183
ﺣﺴﺐ ﻧﻈﺮﯾﺔ ﻣﺴﺘﻘﯿﻢ ﻟﻤﻨﺘﺼﻔﯿﻦ ﻓﺈ ) MN )//( BC ( BC
2
1
= MN
ﺻﻮ B ﺑﺎﻹﻧﺴﺤﺎ ﻟﺬ ﯾﺤ ﻮ M ﻟﻰ N ﻲ H ﻣﻨﺘﺼﻒ ] BC [ ﻷ ﻟﺮﺑﺎﻋﻲ MNHB ﻣﺘﻮ ﺿﻼ
ﺣﻞ ﺗﻤﺮﯾﻦ 15 183
1 ( ﻷﻧﺸﺎ ﻧﺠﺎ ﻟﺸﻜﻞ
2 ( ﺻﻮ ﻟﻤﺜﺚﻠ ABC ﺑﮭﺬ ﻹﻧﺴﺤﺎ
I ﻲ ﺻﻮ A ﺑﻮﺳﻄﺔ ﺬ ﻹﻧﺴﺤﺎ
B' ﻲ ﺻﻮ B ﺑﻮﺳﻄﺔ ﺬ ﻹﻧﺴﺤﺎ
C' ﻲ ﺻﻮ C ﺑﻮﺳﻄﺔ ﺬ ﻹﻧﺴﺤﺎ
ﺻﻮ ﻟﻤﺜﺚﻠ ABC ﺑﮭﺬ ﻹﻧﺴﺤﺎ ﻮ ﻟﻤﺜﺚﻠ IB'C'
3 ( ﻟﺒﺮﺎ ﻋﻠﻰ D ﻣﻨﺘﺼﻒ ] B'C' [
ﻟﺪﯾﻨﺎ ] C'B' [ ﻲ ﺻﻮ ] BC [ ﺑﮭﺬ ﻹﻧﺴﺤﺎ
ﻟﺪﯾﺎﻨ I ﻣﻨﺘﺼﻒ ] BC [ D ﻲ ﺻﻮ I ﺑﮭﺬ ﻹﻧﺴﺤﺎ ﻓﺈ ﺣﺴﺐ ﺧﻮ ﻹﻧﺴﺤﺎ ﻓﺈ
D ﻣﻨﺘﺼﻒ ] B'C' [
4 ( ﻃﺒﯿﻌﺔ ﻟﻤﺜﺚﻠ B'IC'
ﻟﺪﯾﻨﺎ ﻟﻨﻘﻂ D , I , A ﻋﻠﻰ ﺳﺘﻘﺎﻣﺔ ﺣﺪ
ﺣﻠﻮﻝ ﲤﺎﺭﻳﻦ ﺍﻟﻜﺘﺎﺏ ﺍﳌﺪﺭﺳﻲ ﺍﻟﺴﻨﺔ ﺍﻟﺜﺎﻟﺜﺔ ﻣﺘﻮﺳﻂ ﺩﺍﺭ ﻧﺰﻫﺔ ﺍﻷﻟﺒﺏﺎ

8
) CB ) // ( C'B' ( ) AI ( ﻣﺤﻮ ] BC [ ﻓﮭﻮ ﻣﺤﻮ ] C'B' [ ﺬ ﯾﻌﻨﻲ IC' = IB' ﻓﺎﻟﻤﺜﻠﺚ B'IC' ﻣﺘﺴﺎ ﻟﺴﺎﻗﯿﻦ ﮫﺳ I
ﺣﻞ ﺗﻤﺮﯾﻦ 16 183
1 ( ﻟﺸﻜﻞ
2 ( B' ﺻﻮ B ﺑﺎﻻﻧﺴﺤﺎ ﻟﺬ ﯾﺤﻮ A ﻟﻰ C
ACB'B ﻣﺘﻮ ﺿﻼ
C' ﺻﻮ C ﺑﺎﻻﻧﺴﺤﺎ ﻟﺬ ﯾﺤ ﻮ A ﻟﻰ C
) CC' ) // ( AC ( ﺑﺎﻟﺘﺎﻟﻲ ﻟﻨﻘﻂ C' ,C , A
ﺗﻘﻊ ﻋﻠﻰ ﺳﺘﻘﺎﻣﺔ ﺣﺪ ﺑﻤﺎ AC = CC'
ﻓﺈ C ﻲ ﻣﻨﺘﺼﻒ ] AC' [
3 ( ﻧﺒﺮﻦ ﻟﻤﺜﺚﻠ B'C'C ﻗﺎﺋﻢ ﻲﻓ C
ﺑﻤﺎ ﻟﻤﺜﺚﻠ ABC ﻗﺎﺋﻢ ﻲﻓ B
ﻟﺪﯾﻨﺎ ﺻﻮ A ﺑﮭﺬ ﻻﻧﺴﺤﺎ ﻲ C ﺻﻮ C ﻲ C' ﺻﻮ B ﻲ B' ﻓﺎﻟﻤﺜﻠﺚ B'C'C ﻗﺎﺋﻢ ﻲﻓ B' ) ﺣﺴﺐ ﺧﻮ
ﻹﻧﺴﺤﺎ ( ﯾﺤﻔﻆ ﻟﺰﯾﺎ
ﺑﺘﻄﺒﯿﻖ ﻧﻈﺮﯾﺔ ﻓﯿﺜﺎﻏﻮ ﻓﺈ
2
' 'C B +
2
'C B =
2
' CC
2
' 'C B + 16 = 36
16 36 =
2
' 'C B
20 =
2
' 'C B
4.4 = 20 = B'C'
ﺣﻞ ﺗﻤﺮﯾﻦ 17 183
1 ( ﺗﺤﺪﯾﺪ ﻣﺮﻛﺰ ﻟﺪﺋﺮ ) C' ( ﺻﻮ ) C ( ﺑﺎﻹﻧﺴﺤﺎ ﻟﺬ ﯾﺤﻮ O ﻟﻰ A
ﻧﻌﻠﻢ ﺻﻮ ﺋﺮ ﻣﺮﻛﺰﺎ O ﺑﺎﻹﻧﺴﺤﺎ ﻲ ﻟﺪﺋﺮ ﻟﺘﻲ ﻣﺮﻛﺰﺎ ﻲ ﺻﻮ O ﺑﺎﻹﻧﺴﺤﺎ ﻟﻤﺬﻛﻮ ﺣﯿﺚ ﺑﻌﺪ ﻣﺮﻛﺰﺎ
ﻦﻋ O ﻲ ﻧﻔﺴﮭﺎ OA
ﺣﻠﻮﻝ ﲤﺎﺭﻳﻦ ﺍﻟﻜﺘﺎﺏ ﺍﳌﺪﺭﺳﻲ ﺍﻟﺴﻨﺔ ﺍﻟﺜﺎﻟﺜﺔ ﻣﺘﻮﺳﻂ ﺩﺍﺭ ﻧﺰﻫﺔ ﺍﻷﻟﺒﺏﺎ

9
ﻟﺪﺋﺮ ) C' ( ﻣﺮﻛﺰﺎ ﻮ A
2 ( ﺛﺒﺎ ﻟﻨﻘﺔﻄ O ﺗﻨﺘﻤﻲ ﻟﻰ ) C' (
ﻟﻨﻘﺔﻄ A ﻣﺮﺰﻛ ) C' ( OA ﻮ ﻧﺼﻒ ﻗﻄﺮ ﻟﺪﺋﺮ ﻟﺘﻲ ﻣﺮﻛﺰﺎ A ﺬ ﯾﻌﻨﻲ
O ﺗﻨﺘﻤﻲ ﻟﻰ ) C' (
ﺣﻞ ﺗﻤﺮﯾﻦ 18 184
ﻟﺪﯾﻨﺎ O' ﻲ ﺻﻮ O B ﺻﻮ A ﺑﺎﻹﻧﺴﺤﺎ ﻟﺬ ﯾﺤ ﻮ O ﻟﻰ O' ﻓﺎﻟﺮﺑﺎﻲﻋ OO'BA ﻣﺘﻮ ﺿﻼ ﻓﯿﮫ ﻟﻀﻠﻌﯿﻦ
] O'A [ ] O'B [ ﻣﺘﻘﺎﺑﻼ
ﻓﮭﻤﺎ ﻣﺘﻘﺎﯾﺴﺎ OA = O'B
ﺑﻤﺎ A ﻧﻘﻄﺔ ﻣﻦ ﻟﺪﺋﺮ ) C ( ﻟﺪﺋﺮ ) C' ( ﻲ ﺻﻮ ) C ( ﺑ ﮭﺬ ﻹﻧﺴﺤﺎ ﻓﺈ ﺻﻮ A B ﺗﻨﺘﻤﻲ ﻟﻰ ) C' (
ﺣﻞ ﻟﻤﺴﺄﻟﺔ 19 184
1 ( ﺳﻢ ﻟﺸﻜﻞ ﺑﻜﻞ ﻋﻨﺎﯾﺔ ﺔﻗ ) ﺑﺈﺳﺘﻌﻤﺎ ﻷﻟﻮ (
2 ( ﺣﺴﺎ ﻟﻘﯿﺲ B A I
ﻟﻤﺜﺚﻠ ABI ﻣﺘﺴﺎ ﻟﺴﺎﻗﯿﻦ G A I = B A I
ﻷﻧﮭﻤﺎ ﯾﺘﻲ ﻟﻘﺎﻋﺪ
) AB ( ^ ) IG ( ﻟﻤﺜﺚﻠ IAG ﻗﺎﺋﻢ ﻲﻓ G
ﻣﻦ ﻧﻈﺮﯾﺔ ﻓﯿﺜﺎﻏﻮ ﻧﺤﺼﻞ ﻋﻠﻰ IG = 3 cm
ﺑﺎﻟﺘﺎﻟﻲ 0.8 =
5
4
=
AI
AG
= G A I cos = B A I cos
ﺑﺈﺳﺘﻌﻤﺎ ﻟﺤﺎﺳﺒﺔ ﻧﺤﺼﻞ ﻋﻠﻰ 36.86 G A I
ﺳﺘﻨﺘﺎ ﻟﺰﯾﺔ B I A ﻣﻨﻔﺮﺔﺟ
ﻟﻤﺜﺚﻠ AIB ﻣﺘﺴﺎ ﻟﺴﺎﻗﯿﻦ ) ﻓﺮﺎﺿ (
ﻣﻦ ﻟﺤﺴﺎ ﻟﺴﺎﺑﻖ ﻟﺪﯾﻨﺎ
) 73.72 = 36:86 2 = ( G A I + B A I
ﻣﺠﻤﻮ ﯾﺘﻲ ﻟﻘﺎﻋﺪ ﺻﻐﺮ ﻣﻦ ﻟﺰﯾﺔ ﻟﻘﺎﺋﻤﺔ ﯾﺔ ﻟﺮ B I A ﻛﺒﺮ ﻣﻦ ﻟﺰﯾﺔ ﻟﻘﺎﺋﻤﺔ ﻓﮭﻲ ﻣﻨﻔﺮﺔﺟ
ﺣﻠﻮﻝ ﲤﺎﺭﻳﻦ ﺍﻟﻜﺘﺎﺏ ﺍﳌﺪﺭﺳﻲ ﺍﻟﺴﻨﺔ ﺍﻟﺜﺎﻟﺜﺔ ﻣﺘﻮﺳﻂ ﺩﺍﺭ ﻧﺰﻫﺔ ﺍﻷﻟﺒﺏﺎ

10
3 ( ﺗﻌﯿﯿﻦ ﻮﺻ ﻟﻤﺴﺘﻘﯿﻤﺎ ) AH ( ) BH ( ) IH ( ﺑﺎﻹﻧﺴﺤﺎ ﻟﺬ ﯾﺤ ﻮ A ﻟﻰ D
ﻣﻦ ﻟﻤﻌﻠﻮ ﻧﮫ ﻟﺘﺤﺪﯾﺪ ﺻﻮ ﻣﺴﺘﻘﯿﻢ ﺑﺈﻧﺴﺤﺎ ﻣﺎ ﯾﻜﻔﻲ ﺗﺤﺪﯾﺪ ﺻﻮ ﻧﻘﻄﺘﯿﻦ ﻣﻦ ﺬ ﻟﻤﺴﺘﻘﯿﻢ ﻟﺬ ﯾﻜﻔﻲ ﻧﻌﯿﯿﻦ ﻣﻦ ﻞﻛ
ﻣﺴﺘﻘﯿﻢ ﻧﻘﻄﺘﯿﻦ ﺗﺤﺪﯾﺪ ﺻﻮﺗﯿﮭﻤﺎ ﺑﺎﻹﻧﺴﺤﺎ ﻟﻤﺬﻛﻮ ﺗﻌﯿﯿﻦ ﻧﻘﻄﺔ ﻣﻨﺤﻰ ﺛﻢ ﺗﺤﺪﯾﺪ ﺻﻮ ﻟﻨﻘﻄﺔ ﻷ ﻣﻨﺤﻰ ﻟﻤﺴﺘﻘﻢﯿ
ﻣﻌﻠﻮ ﻹﻧﺴﺤﺎ ﯾﺤﺎﻓﻆ ﻋﻠﻰ ﻟﺘﻮ ﯾﺤﺎﻓﻆ ﻋﻠﻰ ﻟﺰﯾﺎ ﯾﺤﺎﻓﻆ ﻋﻠﻰ ﻟﺘﻌﺎﻣﺪ
ﻧﻼﺣﻆ ﻟﻨﻘﺔﻄ H ﻲ ﻧﻘﻄﺔ ﺗﻼﻗﻲ ﺗﻔﺎﻋﺎ ﻟﻤﺜﺚﻠ AIB
ﺗﺤﺪﯾﺪ ﺻﻮ ﻟﻤﺴﺘﻘﻢﯿ ) AH (
) HA ( ﻮ ﺣﺎﻣﻞ ﻹﺗﻔﺎ ﻟﻤﺘﻌﻠﻖ ﺑﺎﻟﻀﻊﻠ ] AI [
) HA ( ^ ) BI (
ﻟﻨﻘﺔﻄ D ﻲ ﺻﻮ A ﺑﺎﻹﻧﺴﺤﺎ ﻟﺬ ﯾﺤﻮ A ﻟﻰ D
A ﻧﻘﺔﻄ ) HA ( ) HA ( ﻋﻤﻮ ﻋﻠﻰ ) BI (
ﺻﻮ ) HA ( ﻮ ﻟﻤﺴﺘﻘﯿﻢ ﻟﺬ ﯾﺸﻞﻤ D ﯾﻮ ) HA ( ) DF (
ﺗﺤﺪﯾﺪ ﺻﻮ ﻟﻤﺴﺘﻘﻢﯿ ) HB (
ﺑﻄﺮﯾﻘﺔﻣﻤﺎﺛﻠﺔ ﻧﺒﺮﻦ ﺻﻮ ) HB ( ﺑﻨﻔﺲ ﻹﻧﺴﺤﺎ ﻮ ) EC ( ﻋﻠﻤﺎ ﺻﻮ B ﻲ C (
ﺗﺤﺪﯾﺪ ﺻﻮ ﻟﻤﺴﺘﻘﻢﯿ ) IH (
ﺻﻮ ﻟﻨﻘﺔﻄ I ﺑﺎﻹﻧﺴﺤﺎ ﻟﻤﻌﻄﻰ ﻲ ﻟﻨﻘﺔﻄ G ﻷ ﻟﺮﺑﺎﻋﻲ IADG ﻣﺘﻮ ﺿﻼ
) ﯾﻤﻜ ﻦ ﺑﺈﺳﺘﻌﻤﺎ ﻧﻈﺮﯾﺔ ﻓﯿﺜﺎﻏﻮ ﺛﺒﺎ ] AD [ ] IG [ ﻣﺘﻘﺎﯾﺴﺘﺎ ﻤﺎ ﯾﻀﺎ ﻣﺘﻮﯾﺎ ﻷﻧﮭﻤﺎ ﻋﻤﻮﯾﺎ ﻋﻠﻰ ) AB (
ﻟﻨﻘﻂ H , G , I ﺗﻘﻊ ﻋﻠﻰ ﺳﺘﻘﺎﻣﺔ ﺣﺪ ﻓﺈ ﺻﻮ ) IH ( ﻲ ) IG ( ﻷ ﻹﻧﺴﺤﺎ ﯾﺤﺎﻓﻆ ﻋﻠﻰ ﺳﺘﻘﺎﻣﯿﺔ ﻟﻨﻘﻂ
ﺻﻮ ) IH ( ﻲ ) IH (
4 ( ﺳﺘﻨﺘﺎ ) CE ( ) DF ( ) IG ( ﻣﺘﻘﺎﻃﻌﺔ
ﻟﻨﻘﺔﻄ H ﻲ ﻧﻘﻄﺔ ﺗﻼﻗﻲ ﻹﺗﻔﺎﻋﺎ ﻟﺜﻼﺛﺔ ﻓﻲ ﻟﻤﺜﺚﻠ AIB ﻟﻤﺴﺘﻘﯿﻤﺎ ) CE ( ) DF ( ) IG ( ﻲ ﺻﻮ ﺗﻔﺎﻋﺎ ﺬ
ﻟﻤﺜﻠﺚ ﺑﺎﻹﻧﺴﺤﺎ
ﻟﻤﺴﺘﻘﯿﻤﺎ ) CE ( ) DF ( ) IG ( ﺗﺘﻼﻗﻰ ﻓﻲ ﻧﻔﺲ ﻟﻨﻘﻄﺔ ﻲ ﺻﻮ H ﺑﮭﺬ ﻹﻧﺴﺤﺎ

ﺣﻠﻮﻝ ﲤﺎﺭﻳﻦ ﺍﻟﻜﺘﺎﺏ ﺍﳌﺪﺭﺳﻲ ﺍﻟﺴﻨﺔ ﺍﻟﺜﺎﻟﺜﺔ ﻣﺘﻮﺳﻂ ﺩﺍﺭ ﻧﺰﻫﺔ ﺍﻷﻟﺒﺏﺎ

11
ﺣﻞ ﻣﺴﺄﻟﺔ 20 184
1 ( ﻟﻨﻘﺔﻄ N' ﻲ ﺻﻮ N ﺎﺑ ﻹﻧﺴﺤﺎ ﻟﺬ ﯾﺤ ﻮ A ﻟﻰ M ﻷ ﻟﺮﺑﺎﻋﻲ AMN'N ﻣﺘﻮ ﺿﻼ
2 ( ﻟﻨﻘﺔﻄ P ﻲ ﻧﻈﯿﺮ M ﺑﺎﻟﻨﺴﺒﺔ ﻟﻰ A ﯾﻤﻜﻦ ﻧﻘﻮ A ﻲ ﺻﻮ P ﺑﻨﻔﺲ ﻹﻧﺴﺤﺎ ﻟﺴﺎﻖﺑ ) ﻻﺣﻆ ﻟﻨﻘﻂ P
A M ﺗﻘﻊ ﻋﻠﻰ ﺳﺘﻘﺎﻣﺔ ﺣﺪ (
A' ﻧﻈﯿﺮ N ﺑﺎﻟﻨﺴﺒﺔ ﻟﻰ A AA' = NA
) NA ) // ( AA' (
3 ( ﻧﺸﺎ ﻟﻨﻘﺔﻄ P' ﻟﺘﻲ ﺻﻮﺗﺎﮭ A' ﺑﺎﻹﻧﺴﺤﺎ ﻟﺬ ﯾﺤ ﻮ A ﻟﻰ M
ﻟﻨﻘﺔﻄ A' ﻲ ﺻﻮ P' ﺑﺎﻹﻧﺴﺤﺎ ﻟﻤﺬﻛﻮ ﻣﻨﮫ ﻟﺮﺑﺎﻋﻲ P'A'MA ﻣﺘﻮ ﺿﻼ
4 ( ﻟﺪﯾﻨﺎ A ﺻﻮ P A' ﺻﻮ P' ﺑﻮﺳﻄﺔ ﻧﻔﺲ ﻹﻧﺴﺤﺎ ﻟﺮﺑﺎﻋﻲ AA'P'P ﻣﺘﻮ ﺿﻼ
5 ( ﻹﻧﺴﺤﺎ ﻟﺬ ﯾﺤﻮ A' ﻟﻰ M ﯾﺤﻮ P' ﻟﻰ A ﻷ ﻟﺮﺑﺎﻋﻲ A'MAP' ﻣﺘﻮ ﺿﻼ
ﺣﺴﺐ ﻟﺒﺮﺎ ﻟﺜﺎﺚﻟ
ﺬ ﻹﻧﺴﺤﺎ ﯾﺤ ﻮ ﯾﺎﻀ A ﻟﻰ N' ﯾ ﻮﺤ P ﻟﻰ N ﻷ ﻟﺮﺑﺎﻋﻲ PAN'N ﻣﺘﻮ ﺿﻼ
ﻧﺮﺗﺐ ﺬ ﻟﻨﺘﺎﺋﺞ ﻛﺎﻵﺗﻲ :
ﻹﻧﺴﺤﺎ ﻟﺬ ﯾﺤ ﻮ A' ﻟﻰ M ﯾﺤ ﻮ ﯾﺎﻀ
M A'
A P'
N P
N' A
ﻟﺮﺑﺎﻋﻲ MANN' ﻮ ﺻﻮ ﻟﺮﺑﺎﻋﻲ A'P'PA ﺑﮭﺬ ﻹﻧﺴﺤﺎ
ﺑﻤﺎ ﻹﻧﺴﺤﺎ ﯾﺤﻔﻆ ﻷﺷﻜﺎ ﺑﻤﺎ MANN' ﻮ ﻣﺘﻮ ﺿﻼ ﻓﺈ A'P'PA ﯾﺎﻀ " ﻣﺘﻮ ﺿﻼ
ﻋﻠﻤﺎ ﻹﻧﺴﺤﺎ ﯾﺤﻔﻆ ﻟﻤﺴﺎﺣﺎ ﻓﺈ ﻟﺮﺑﺎﻋﯿﺎ ﻟﮭﻤﺎ ﻧﻔﺲ ﻟﻤﺴﺎﺣﺔ

ﺣﻠﻮﻝ ﲤﺎﺭﻳﻦ ﺍﻟﻜﺘﺎﺏ ﺍﳌﺪﺭﺳﻲ ﺍﻟﺴﻨﺔ ﺍﻟﺜﺎﻟﺜﺔ ﻣﺘﻮﺳﻂ ﺩﺍﺭ ﻧﺰﻫﺔ ﺍﻷﻟﺒﺏﺎ

12

ﺣﻞ ﻧﺸﺎ ) 1 ( 185 ﻣﻦ ﺧﺘﺒﺮ ﻣﻜﺘﺴﺒﺎﻚﺗ
1 ( ﻟﺘﻤﻌﻦ ﻲﻓ ﻟﻤﺠﺴﻤﺎ
2 (
ﻟﻤﺠﻢﺴ ﺳﮫﻤ ﻋﺪ
ﻷﺟﮫ
ﻟﺠﺎﻧﺒﺔﯿ
ﻋﺪ
ﻗﻮﻋﺪ
ﻋﺪ
ﻷﺣﺮ
ﻟﺠﺎﻧﺒﺔﯿ
ﻋﺪ
ﻷﺣﺮ
ﻟﻜﻠﺔﯿ
ﻋﺪ
ﺳﮫ
) 1 (

ﻣﺴﺘﻄﯿﻼ
6 2 4 12 8
) 2 (
ﺳﻄﻮﻧﺔ

2 2 0 0 0
) 3 (
ﻣﻮﺷﻮ
ﻗﺎﻢﺋ
7 2 5 15 10
ﻧﺸﺎ ) 1 ( 186
1 ( ﻧﻌﻢ
ﻟﺼﻮ ﻲ êﺮﻣﺎ ﻟﺠﯿﺰ ﺑﻤﺮﺼ
2 ( ﻷﺷﯿﺎ ﻟﻮ ﻓﻲ ﻟﻮﺼ ﻲ ﻣﺠﺴﻤﺎ ﻣﺮﻛﺒﺔ
ﻧﺸﺎ ) 2 ( 186
1 ( ﺻﻒ ﻛﻞ ﻣﻦ ﻟﮭﺮ ﻟﻤﻮﺷﻮ ﻟﻘﺎﻢﺋ
ﻋﻨﺎﺻﺮ ﻟﺘﺸﺎﺑﮫ ﺑﯿﻨﮭﻤﺎ ﻲ : ﻟﻘﻮﻋﺪ ﻷﺟﮫ ﻟﺠﺎﻧﺒﯿﺔ ﻟﻜﻞ ﻣﻦ ﻟﻤﺠﺴﻤﯿﻦ ﻲ ﻣﻀﻠﻌﺎ
ﻋﻨﺎﺻﺮ ﻹﺧﺘﻼ
ﻟﮭﺮ ﻟﻤﻮﺷﻮ ﻟﻘﺎﻢﺋ
ﻗﺎﻋﺪﺗﮫ ﺣﺪ ) ﻲ ﻣﻀﻊﻠ ( ﻗﺎﻋﺘﺎ ) ﻤﺎ ﻣﻀﻠﻌﺎ (
ﺣﻠﻮﻝ ﲤﺎﺭﻳﻦ ﺍﻟﻜﺘﺎﺏ ﺍﳌﺪﺭﺳﻲ ﺍﻟﺴﻨﺔ ﺍﻟﺜﺎﻟﺜﺔ ﻣﺘﻮﺳﻂ ﺩﺍﺭ ﻧﺰﻫﺔ ﺍﻷﻟﺒﺏﺎ

13
ﺟﮭﮫ ﻟﺠﺎﻧﺒﯿﺔ ﻣﺜﻠﺜﺎ ﺟﮭﮫ ﻟﺠﺎﻧﺒﯿﺔ ﻣﺴﺘﻄﯿﻼ
ﺎﻷﺟﮫ ﻟﺠﺎﻧﺒﯿﺔ ﺗﺸﺘﺮ ﺟﮫ ﻟﺠﺎﻧﺒﯿﺔ ﻋﻤﻮﯾﺔ ﻋﻠﻰ
ﻓﻲ ﺣﺪ ﻟﻘﺎﻋﺪﺗﯿﻦ
2 ( s ﻗ ﻤﺔ ﻟﮭﺮ SC SB ﺣﺮ ﻟﮭﺮ ﻟﺮﺑﺎﻋﻲ ABCD ﻗ ﺎﻋﺪ ﻟﮭﺮ A D ﻟﮭﺮ ﻟﻤﺜﺚﻠ SAB ﺟﮫ
ﺟﺎﻧﺒﻲ
ﻟﺸﻜﻞ ﻟﮭﻨﺪﺳﻲ ﻟﻘﺎﻋﺪ ﺬ ﻟﮭﺮ ﻮ ﻣﻀﻊﻠ
ﻷﺷﻜﺎ ﻟﮭﻨﺪﺳﯿﺔ ﻟﻤﺸﻜﻠﺔ ﻟﻠﺴﻄﺢ ﻟﺠﺎﻧﺒﻲ ﻟﮭﺬ ﻟﻤﺠﺴﻢ ﻲ ﻣﺜﻠﺜﺎ
ﻧﺸﺎ ) 3 ( 186
1 ( êﺮﻣﺎ ﺗﻔﺎﻋﮭﺎ ﯾﺸﻤﻞ ﻟﮭﺮ ﻣﺮﻛﺰ ﻗﺎﻋﺪﺗﮫ ﻣﺜﻞ ﻟﮭﺮ ) 1 (
êﺮﻣﺎ ﺗﻔﺎﻋﮭﺎ ﯾﺸﻤﻞ ﻟﮭﺮ ﻻ ﯾﺸﻤﻞ ﻣﺮﻛﺰ ﻟﻘﺎﻋﺪ ﻣﺜﻞ ﻟﮭﺮ ) 2 (
2 ( êﺮﻣﺎ ﻗﺎﻋﺪﺗﮭﺎ ﻣﻀﻠﻊ ﻣﻨﺘﻈﻢ ) ﻗﺎﻋﺪ ﻟﮭﺮ ) 1 ( ﻣﺮﻊﺑ (
êﺮﻣﺎ ﻗﺎﻋﺘﮭﺎ ﻟﯿﺴﺖ ﻣﻀﻠﻊ ﻣﻨﺘﻈﻢ ) ﻗﺎﻋﺪ ﻟﮭﺮ ) 3 ( ﻣﺴﺘﻄﻞﯿ (
ﯾﺘﻢ ﻟﺘﻤﯿﯿﺰ ﻓﻲ ﺬ ﻟﺴﺆ ﯾﻀﺎ ﺑﯿﻦ ﻟﻤﺜﻠﺜﺎ ﻟﻤﺸﻜﻠﺔ ﻟﻸﺟﮫ ﻟﺠﺎﻧﺒﯿﺔ ﻟﻜﻞ ﻣﻦ ﻟﮭﺮﻣﯿﻦ .
ﻓﻲ ﻟﮭﺮ ) 1 ( ﻛﻞ ﻟﻤﺜﻠﺜﺎ ﻣﻘﺎﯾﺔﺴ
ﻓﻲ ﻟﮭﺮ ) 2 ( ﻟﻤﺜﻠﺜﺎ ﻛﻠﮭﺎ ﻣﻘﺎﯾﺔﺴ
3 ( ﻓﻲ ﺬ ﻟﺴﺆ ﻗﺒﻞ ﺗﻤﺎ ﻟﻨﺺ ﯾﻄﻠﺐ ﺗﻌﻠﯿﻞ ﺗﻘﺎﯾﺲ ﻟﻤﺜﻠﺜﺎ ﻟﻤﺸﻜﻠﺔ ﻟﻸﺟﮫ ﻟﺠﺎﻧﺒﯿﺔ ﻟﻠﮭﺮ ) 1 ( ﻟﺬ ﻗﺎﻋﺪﺗﮫ ﻣﺮﺑﻊ ﻋﺪ
ﺗﻘﺎﯾﺲ ﻟﻤﺜﻠﺜﺎ ﻟﻤﺸﻜﻠﺔ ﻟﻸﺟﮫ ﻟﺠﺎﻧﺒﯿﺔ ﻟﻠﮭﺮ ) 2 ( ﻟﺬ ﻗﺎﻋﺪﻧﮫ ﻣ ﺴﺘﻄﯿﻞ
ﯾﻤﻜﻦ ﻟﻚ ﻋﻠﻰ ﺷﻜﻞ ﺗﻤﺮﯾﻦ
* ﻗﺎﻋﺪ ﻟﮭﺮ ) 1 ( ﻣﻀﻠﻊ ﻣﻨﺘﻈﻢ ) ﻣﺮﻊﺑ ( ﺗﻔﺎﻋﮫ ﯾﺸﻤﻞ ﻣﺮﻛﺰ ﻟﻘﺎﻋﺪ ﻧﻘﻮ ﻧﮫ ﺮ ﻣﻨﺘﻈﻢ
* ﺟﮭﮫ ﻟﺠﺎﻧﺒﯿﺔ ﻣﺜﻠﺜﺎ ﻣﺘﻘﺎﯾﺴﺔ ﻣﺘﺴﺎﯾﺔ ﻟﺴﺎﻗﯿﻦ
4 ( ﻟﮭﺮﻣﯿﻦ ) b ( ) c ( ﻣﻨﺘﻈﻤﯿﻦ
) b ( ﻗﺎﻋﺘﮫ ﻣﺮﺑﻊ ﺗﻔﺎﻋﮫ ﯾﺸﻤﻞ ﻣﺮﻛﺰ ﻟﻘﺎﻋﺪ
) c ( ﻗﺎﻋﺘﮫ ﻣﺜﺚﻠ ﻣﺘﻘﺎﯾﺲ ﻷﺿﻼ ﺗﻔﺎﻋﮫ ﯾﺸﻤﻞ ﻣﺮﻛﺰ ﻟﻘﺎﻋﺪ
ﻣﺎ ﻟﮭﺮﻣﯿﻦ ) a ( ) d ( ﻓﮭﻤﺎ ﻟﯿﺲ ﻣﻨﺘﻈﻤﯿﻦ ﻷ ) ﺗﻔﺎﻋﯿﮭﻤﺎ ﻻ ﯾﺸﻤﻼ ﻣﺮﻛﺰ ﻟﻘﺎﻋﺪ
ﺣﻠﻮﻝ ﲤﺎﺭﻳﻦ ﺍﻟﻜﺘﺎﺏ ﺍﳌﺪﺭﺳﻲ ﺍﻟﺴﻨﺔ ﺍﻟﺜﺎﻟﺜﺔ ﻣﺘﻮﺳﻂ ﺩﺍﺭ ﻧﺰﻫﺔ ﺍﻷﻟﺒﺏﺎ

14
ﻣﻨﺎﻗﺸﺔ ﺗﻤﺮﯾﻦ ) 1 ( 201
ﻟﻤﺠﺴﻤﺎ ﻟﺒﺴﯿﻄﺔ ﻲ :
) 1 ( ﺮ ﻗﺎﻋﺘﮫ ﻣﺜﻠﺚ ﻣﺘﻘﺎﯾﺲ ﻷﺿﻼ
) 3 ( ﻣ ﻮﺷﻮ ﻗﺎﻢﺋ ) 5 ( ﺮ ﻗﺎﻋﺘﮫ ﻣﺮﻊﺑ ) 6 ( ﺮ ﻗﺎﻋﺘﮫ ﺜﻣ ﺚﻠ
ﻟﻤﺠﺴﻤﺎ ﻟﻤﺮﻛﺒﺔ ﻲ :
) 2 ( ﺳﻄﻮﻧﺔ ﻏﻄﺎﺋﮭﺎ ﻣﺨﺮ ) 4 ( ﻣﺘﻮ ﻣﺴﺘﻄﯿﻼ ﻏﻄﺎﺋﮫ ﺮ
ﻧﺸﺎ ) 1 ( 187
1 ( ﻟﻤﺠﺴﻤﺎ ﻟﻤﺮﻛﺒﺔ ﯾﻄﻠﺐ ﺻﻒ ﻛﻞ ﻣﻨﮭﺎ ﻣﻊ ﻛﺮ ﺳﻢ ﻛﻞ ﻣﺠﺴﻢ ﻣﻦ ﻟﻤﺠﺴﻤﺎ ﻟﺘﻲ ﯾﺘﺮﻛﺐ ﻣﻨﺎﮭ
2 ( ﻣﻄﺎﻟﺒﺔ ﻟﺘﻼﻣﯿﺬ ﻛﺮ ﺷﯿﺎ ﺧﺮ ﻟﮭﺎ ﺷﻜﻞ ﻣﺨﺮ
ﻧﺸﺎ ) 2 ( 188
1 ( ﻋﻨﺎﺻﺮ ﻟﺘﺸﺎﺑﮫ : ﻲ ﻗﺎﻋﺪ ﻛﻞ ﻣﻨﮭﻤﺎ ﻋﺒﺎ ﻋﻦ ﻗﺮ
ﻋﻨﺎﺻﺮ ﻹﺧﺘﻼ
ﺳﻄﻮﻧﺔ ﻣﺨﺮ
ﻗﺎﻋﺘﯿﻦ ﻛﻞ ﺣﺪɪﻲ ﻗﺮ ﻗﺎﻋﺪ ﺣﺪɪﻲ ﻗﺮ
ﺟﮫ ﻟﺠﺎﻧﺒﯿﺔ ﻋﻤﻮﯾﺔ ﻋﻠﻰ ﻷﺟﮫ ﻟﺠﺎﻧﺒﯿﺔ ﺗﺸﺘﺮ
ﻟﻘﺎﻋ ﺪﺗﯿﻦ ﻓﻲ ﺪﺣ
2 ( ﻟﻤﺨﺮ ﻟﻮﺟﮫ ﻟﺠﺎﻧﺒﻲ ﻟﻘﺎﻋﺪ
ﻟﺸﻜﻞ ﻟﮭﻨﺪﺳﻲ ﻟﻠﺴﻄﺢ ﻟﺠﺎﻧﺒﻲ ﻟﻠﻤﺠﺴﻢ ﻮ ﺳﻄﺢ ﻣﻨﻦﺤ
ﻟﺸﻜﻞ ﻟﮭﻨﺪﺳﻲ ﻟﻘﺎﻋﺪ ﺬ ﻟﻤﺠﺴﻢ ﻮ ﻗﺮ
ﻧﺸﺎ ) 3 ( 188
ﺣﻠﻮﻝ ﲤﺎﺭﻳﻦ ﺍﻟﻜﺘﺎﺏ ﺍﳌﺪﺭﺳﻲ ﺍﻟﺴﻨﺔ ﺍﻟﺜﺎﻟﺜﺔ ﻣﺘﻮﺳﻂ ﺩﺍﺭ ﻧﺰﻫﺔ ﺍﻷﻟﺒﺏﺎ

15
1 ( ﻟﺸﻜﻞ ﻟﮭﻨﺪﺳﻲ ﻟﺬ ﺗﺮﺳﻤﮫ ﻟﻨﻘﻄﺔ ﻮ ﺋﺮ
[ OS 2 ( ﺗﻔﺎ ﻟﻤﺨﺮ ) 5 ( ﻮ ﻟﻘﻄﺔﻌ ]
( d ﻟﻲﺘ ﺣﺎﻣﻠﮭﺎ ﻟﻤﺴﺘﻘﻢﯿ )
SM=SM' ﻹﺛﺒﺎ
ﻣﺘﻘﺎﯾﺴﺎ SOM , SOM' ﻧﺜﺒﺖ ﻟﻤﺜﻠﺜﻦﯿ
ﻛﻞ ﻣﻮﻟﺪ ﻟﻤﺨﺮ ﻣﻘﺎﯾﺔﺴ
ﻧﺸﺎ ) 1 ( 189
ﻟﻢ ﺗﺴﺘﻌﻞﻤ ) ﻓﻲ ﻞﻛ ﻷﻣﺎﻛﻦ ﻟﺘﻲ ﯾﺠﺐ ﺳﺘﻌﻤﺎﻟﮭﺎ ( ﺗﻘﻨﯿﺔ ﻟﻤﻨﻈﻮ ﻟﻤﺘﺴﺎ ﻟﻘﯿﺎ . ﻧﻈﺮ ﻟﺸﻜﻞ ) 1 (
ﻟﺤﺮ ] SD [ ﯾﻜﻮ ﻣﻨﻘﻄﺎ ﻷﻧﮫ ﺧﻠﻒ ﻟﻮﺟﮭﯿﻦ SAB SAC
ﻣﺨﺮ ﻟﺪ ﻟﺸﻜﻞ ) 2 ( ﯾﺤﺘﻤﻞ ﺟﺎﺑﺘﯿﻦ ﻟﻚ ﺣﺴﺐ ﻣﻮﻗﻊ ﻟﺮﺔﯾ
ﻛﺎﻧﺖ ﻟﺮﯾﺔ ﻣﻦ ﻷﺳﻔﻞ ﻓﺈ ﻟﺮﺳﻢ ﺻﺤﺢﯿ
ﻛﺎﻧﺖ ﻟﺮﯾﺔ ﻣﻦ ﻟﺠﺎﺐﻧ ﻓﺈ ﻟﺮﺳﻢ ﻟﯿﺲ ﺻﺤﯿﺤﺎ
ﺟﺰ ﻣﻦ ﻟﻘﺎﻋﺪ ﻻ ﯾﺮ ﻷﻧﮫ ﯾﻘﻊ ﺧﻠﻒ ﻟﺴﻄﺢ ﻟﺠﺎﻧﺒﻲ
ﻧﺸﺎ ) 2 ( 189
1 ( ﻻ ﺗﺮ ﻛﻞ ﺟﺰ ﺬﯾﻦ ﻟﻤﺠﺴﻤﻦﯿ
2 ( ﺳﻢ ﺮ ﻣﻨﺘﻈﻢ ﺑﺤﯿﺚ ﯾﻜﻮ ﻛﻞ ﺟﺰ ﻻ ﯾﺮ ﻣﻨﻂﻘ
ﻧﺸﺎ ) 2 ( ﻣﻦ ﺧﺘﺒﺮ ﻣﻜﺘﺴﺒﺎﻚﺗ
) 1 ( ﻟﺘﺼﻤﯿﻤﺎ ﻟﺼﺤﯿﺤﺎ ﻤﺎ a c
ﻷﺧﻄﺎ ﻟﻮ ﻓﻲ ﻟﺘﺼﻤﯿﻢ ﻟﺨﺎﺊﻃ b ﻮ ﻟﻘﺎﻋﺪﺗﯿﻦ ﻓﻲ ﻧﻔﺲ ﻟﺠﮭﺔ ﺣﺘﻰ ﯾﻜﻮ ﺻﺤﯿﺢ ﻧﺮﺳﻢ ﻟﻤﺜﻠﺚ ﻟﺜﺎﻧﻲ ﻓﻲ ﺟﮭﺔ
ﺧﺮ ﻟﻌﺮ ﻟﻤﺴﺘﻄﻞﯿ
ﺣﻠﻮﻝ ﲤﺎﺭﻳﻦ ﺍﻟﻜﺘﺎﺏ ﺍﳌﺪﺭﺳﻲ ﺍﻟﺴﻨﺔ ﺍﻟﺜﺎﻟﺜﺔ ﻣﺘﻮﺳﻂ ﺩﺍﺭ ﻧﺰﻫﺔ ﺍﻷﻟﺒﺏﺎ

16
) 2 ( ﻟﺘﺼﻤﯿﻢ ﻟﺼﺤﯿﺢ ﻮ : g
ﻷﺧﻄﺎ ﻟﻮ ﻓﻲ ﻟﺘﺼﻤﯿﻢ f ﻮ ﻟﻘﺎﻋﺪ ﻣﺮﺳﻮﻣﺔ ﻓﻲ ﻷﻋﻠﻰ ﺣﺘﻰ ﯾﻜﻮ ﻟﺘﺼﻤﯿﻢ ﺻﺤﯿﺢ ﺗﺮﺳﻢ ﻟﻘﺎﻋﺪ ﻓﻲ ﻟﺎﺠ ﻧﺐ
ﻟﯿﺲ ﺳﻞﻔ
ﻟﺨﻄﺄ ﻟﻮ ﻓﻲ ﻟﺘﺼﻤﯿﻢ h ﻟﻘﺎﻋﺪﺗﯿﻦ ﻏﯿﺮ ﻣﺮﺳﻮﻣﯿﻦ ﻓﻲ ﺟﺎﻧﺒﻲ ﻟﻤﺴﺘﻄﻞﯿ
ﻧﺸﺎ ) 1 ( 192
ﻣﻼﺣﻈﺔ : ﺗﻜﻮ ﻷﻧﺸﻄﺔ ﻣﺤﻀﺮ ﻓﻲ ﻟﺒﯿﺖ
1 ( ﺣﺴﻦ ﻃﺮﯾﻘﺔ ﻟﻠﺤﺼﻮ ﻋﻠﻰ ﺗﺼﻤﯿﻢ ﻣﺠﺴﻢ ﻮ ﻹﻧﻄﻼ ﻣﻦ ﻣﺠﺴﻢ ﺣﻘﯿﻘﻲ ﯾﺴﺘﺤﺴﻦ ﺳﺘﻌﻤﺎ ﻷﻟﻮ ﻟﺘﻌﯿﯿﻦ ﺿﻼ
ﻷﺷﻜﺎ ﻟﻨﺎﺗﺠﺔ ﻋﻦ ﻧﻔﺲ ﻟﺤﺮ ) ﻧﻔﺲ ﻟﻠﻮ ﻟﻨﻔﺲ ﻟﺤﺮ (
ﺬ ﻗﺒﻞ ﻧﺸﺮ ﺟﮫ ﻛﻞ ﻣﻦ ﻣﺠﺴﻤﻲ ﻟﺴﺆﻟﻦﯿ 1 2 ﻣﻦ ﻟﻨﺸﺎ
3 ( ﻟﺘﺼﻤﯿﻢ ﻟﻮﺣﯿﺪ ﻟﺬ ﯾﻤﺜﻞ ﺗﺼﻤﯿﻤﺎ ﻟﻤﺨﺮ ﻧﻲ ﻮ ﻟﺘﺼﻤﯿﻢ ) 3 (
ﺑﺎﻟﻨﺴﺒﺔ ﻟﻠﺘﺼﻤﯿﻢ ) 1 ( ﺪﻋ ) ﺑﻔﺼﻞ ﻟﻘﺮ ﻋﻦ ﻣﻜﺎﻧﮫ ﻣﺜﻼ ( ﻧﺤﺼﻞ ﻋﻠﻰ ﺗﺼﻤﯿﻢ ﻟﻤﺨﺮ ﻲﻧ
ﻧﺸﺎ ) 2 ( 193
ﻲﻓ ﻟﺘﺼﺎﻣﯿﻢ ﻟﻤﻘﺪﻣﺔ ﻓﻲ ﻛﺘﺎ ﺗﻠﺘﻠﻤﯿﺬ ﺧﻠﻞ ﺗﻘﻨﻲ ﻟﺬ ﯾﻌﺎ ﺗﻘﺪﯾﻤﮭﺎ ﻓﻲ ﻟﺪﻟﻞﯿ
1 ﻟﺘﺼﻤﯿﻤﺎ ) 1 ( ) 2 ( ﻤﺎ ﺗﺼﻤﯿﻤﺎ ﻟﮭﺮﻣﯿﻦ ﻣﻨﺘﻈﻤﯿﻦ ﯾﻄﻠﺐ ﻣﻦ ﻟﺘﻼﻣﯿﺬ ﺗﻌﻠﯿﻞ ﻟﻚ
ﻟﺘﺼﻤﯿﻢ ) 3 ( ﻟﯿﺲ ﺗﺼﻤﯿﻤﺎ ﻟﮭﺮ ﯾﻄﻠﺐ ﺗﻌﻠﯿﻞ ﻟﻚ .
ﯾﻤﻜﻦ ﻟﺤﺼﻮ ﻋﻠﻰ ﺗﺼﻤﯿﻢ ﻟﮭﺮ ﻣﻨﺘﻈﻢ ﺑﺘﻌﺪﯾﻞ ﻃﻔﯿﻒ ﻟﻤﻮﻗﻊ ﺑﻌﺾ ﻷﺟﮫ ﻓﯿﮫ
ﻟﺘﺼﻤﯿﻢ ) 4 ( ﻟﯿﺲ ﺗﺼﻤﯿﻤﺎ ﻟﮭﺮ ﻣﻨﺘﻈﻢ ﯾﻄﻠﺐ ﺗﻌﻠﯿﻞ ﻟﻚ
2 ﯾﻤﻜﻦ ﻹﻋﺘﻤﺎ ﻋﻠﻰ ﺣﺪ ﺗﺼﺎﻣﯿﻢ ﻟﺴﺆ ﻟﺴﺎﻖﺑ
ﺗﺮ ﻟﺤﺮﯾﺔ ﻟﻠﺘﻠﻤﯿﺬ ﻓﻲ ﻧﺠﺎ ﺗﺼﻤﯿﻢ ﺧﺮ ﻋﻠﻰ ﯾﻜﻮ ﺑﺎﻷﻃﻮ ﻟﻤﻄﻠﻮﺑﺔ ﺛﻢ ﯾﺼﻨﻊ ﺬ ﻟﮭﺮ
ﻧﺸﺎ ) 3 ( 193
ﯾﺘﺒﯿﻦ ﻟﺘﻠﻤﯿﺬ ﻓﻲ ﻟﻨﺸﺎ ) 1 ( ﻣﻦ ﻟﻔﻘﺮ ﻟﻠﺘﻮﻇﯿﻒ ﻟﺴﻄﺢ ﻟﺠﺎﻧﺒﻲ ﻟﻤﺨﺮ ﻧﻲ ﻮ ﻗﻄﺎ ﻗﺮ
1 ﻓﻲ ﺣﺎﻟﺔ ﻇﮭﻮ ﺻﻌﻮﺑﺔ ﻣﺎ ﻟﺪ ﺑﻌﺾ ﻟﺘﻼﻣﯿﺬ ﯾﻤﻜﻦ ﺳﻢ ﻟﻤﺨﺮ ﻋﻠﻰ ﻟﺴﺒﻮ ﺑﺮ ﻋﻠﻰ ﺬ ﻟﻤﺨﺮ ﻟﻤﺜﺚﻠ
SOM ﺑﺎﻠﻟ ﻮ ﻷﺣﻤﺮ ﻛﺬﻟﻚ ﻣﺰ ﻟﺰﯾﺔ ﻟﻘﺎﺋﻤﺔ ﻋﻨﺪ ﻟﺮ O ﺑﮭﺬ ﻗﺪ ﯾﮭﺘﺪ ﻟﺘﻠﻤﯿﺬ ﻟﻰ ﻹﺟﺎﺑﺔ ﻋﻠﻰ ﻟﺴﺆ
ﺣﻠﻮﻝ ﲤﺎﺭﻳﻦ ﺍﻟﻜﺘﺎﺏ ﺍﳌﺪﺭﺳﻲ ﺍﻟﺴﻨﺔ ﺍﻟﺜﺎﻟﺜﺔ ﻣﺘﻮﺳﻂ ﺩﺍﺭ ﻧﺰﻫﺔ ﺍﻷﻟﺒﺏﺎ

17
2 ﻓﻲ ﻟﻔﺮ ﻷ ﻣﻦ ﻟﺴﺆ ﯾﻄﻠﺐ ﺷﺮ ﺳﺒﺐ ﺗﺴﺎ ﻃﻮ ﻗﻮ C B
)
ﻣﺤﯿﻂ ﻗﺮ ﻟﻘﺎﻋﺪ ﺛﻢ ﯾﻄﻠﺐ ﺳﺘﻨﺘﺎ ﻃﻮ
ﺬ ﻟﻘﻮ
* ﯾﻤﻜﻦ ﻹﻧﻄﻼ ﻣﻦ ﻣﺨﺮ ﻟﺪ ﺗﺒﺎ ﻣﺮﺣﻞ ﻧﺸﺮ ﺑﺎﻟﻘﺺ ﻣﺜﻠﻤﺎ ﻮ ﻓﻲ ﻟﺴﺆ ) 2 ( ﻣﻦ ﻟﻨﺸﺎ ) 1 (
ﻟﻠﻮﺻﻮ ﻋﻤﻠﯿﺎ ﻟﻰ ﻓﮭﻢ ﺳﺒﺐ ﺗﺴﺎ ﻃﻮ ﻟﻘﻮ C B
)
ﻣﻊ ﻣﺤﯿﻂ ﻗﺮ ﻟﻘﺎﻋﺪ ) ﻋﻨﺪ ﻣﺤﺎﻟﺔ ﻟﺤﺼﻮ ﻋﻠﻰ ﺗﺼﻤﯿﻢ
ﻟﻤﺨﺮ ﻟﺪﻧﻲ ﺳﻮ ﯾﻼﺣﻆ ﻗﻮ ﻗﻄﺎ ﻟﻘﺮ ﻟﺴﻄﺢ ﻟﺠﺎﻧﺒﻲ ﻣﺘﻄﺎﺑﻖ ﻣﻊ ﻣﺤﯿﻂ ﻗﺮ ﻟﻘﺎﻋﺪ (
ﺑﻤﺎ ﻃﻮ ﻟﻘﻮ C B
)
ﯾﺴﺎ ﻣﺤﻂﯿ ﻗﺮ ﻟﻘﺎﻋﺪ ﻓﺈ ﻃﻮ ﻟﻘﻮ C B
)
ﻮ cm p 12 = cm p 6 2
ﻓﻲ ﻟﻔﺮ ﻟﺜﺎﻟﺚ ﻣﻦ ﻟﺴﺆ ) ﺑﻮﺿﻊ ﻟﺤﺮ S ﺑﺪﻻ ﻦﻣ A ( ﯾﺘﯿﺒ ﻦ ﻟﻠﺘﻠﻤﯿﺬ ﻣﻌﺮﻓﺔ ﻃﻮ ﻗﻮ ﻟﺴﻄﺢ ﻟﺠﺎﻧﺒﻲ ﻟﻠﻤﺨﺮ
ﻻﯾﻜﻔﻲ ﻟﻠﺤﺼﻮ ﻋﻠﻰ ﻟﺴﻄﺢ ﻟﺠﺎﻧﺒﻲ ﻟﮭﺬ ﻟﻤﺨﺮ
ﻣﺤﯿﻂ ﻟﻘﺮ ) ﻃﻮ ﻟﺪﺋﺮ ( ﻟﺘﻲ ﻣﺮﻛﺰﺎ S ﻧﺼﻒ ﻗﻄﺮﺎ 10cm ﻮ cm p 20 = cm p 10 2
ﻛﺎ x ﻮ ﻗﯿﺲ ﯾ ﺔ ﻟﻘﻄﺎ ﻓﺈﻧﻨﺎ ﻧﺤﺼﻞ ﻋﻠﻰ ﺟﺪ ﻟﺘﻨﺎﺳﺒﯿﺔ
216 =
p
p
20
360 12
= x
ﺑﺎﻟﺘﺎﻟﻲ ﻗﯿﺲ ﻟﺰﯾﺔ ﻟﻤﺮﻛﺰﯾﺔ ﻟﻠﻘﻄﺎ ﻟﺘﻲ ﺗﺤﺼﺮ ﻟﻘﻮ C B
)
ﻮ 216
ﺑﺎﻻﻋﺘﻤﺎ ﻋﻠﻰ ﻟﻤﻌﻠﻮﻣﺎ ﻟﺘﻲ ﺳﺘﻨﺘﺠﺖ ﻣﻦ ﻟﺴﺆ ﻟﺴﺎﺑﻖ ﯾﻤﻜﻦ ﻧﺠﺎ ﺗﺼﻤﯿﻢ ﻟﻠﻤﺨﺮ ﻟﻤﻄﻠﻮ
ﯾﺘﻜﻮ ﺬ ﻟﺘﺼﻤﯿﻢ ﻦﻣ
ﻗﺎﻋﺪ ﻲ ﻗﺮ ﻗﻄﺮ 6cm
ﺳﻄﺢ ﺟﺎﻧﺒﻲ ﻮ ﻗﻄﺎ ﻗﺮ ﻗﯿﺲ ﯾﺘﮫ ﻟﻤﺮﻛﺰﺔﯾ 216 ﻧﺼﻒ ﻗﻄﺮ 10cm ﻟﺼﻨﻊ ﻟﻤﺨﺮ ﻟﻤﻄﻠﻮ ﺑﺴﮭﻮﺔﻟ
ﯾﺴﺘﺤﺴﻦ ﺗﺮ ﺷﺮﻃﺔ ﻟﺼﻖ ﻋﻠﻰ ﻟﺘﺼﻤﯿﻢ
4 ﯾﺘﻮﺻﻞ ﻟﺘﻠﻤﯿﺬ ﻋﺒﺮ ﺬ ﻟﺴﺆ ﻟﻰ ﻋﻼﻗﺔ ﺑﺴﯿﻄﺔ ﺗﺴﻤﺢ ﻟﮫ ﺑﺤﺴﺎ ﻗﯿﺲ ﻟﺰﯾﺔ ﻟﻤﺮﻛ ﺰﯾﺔ ﻟﺴﻄﺢ ﻟﺠﺎﻧﺒﻲ ﻟﻤﺨﺮ
ﻲﻧ
ﺑﺎﺳﺘﻌﻤﺎ ﻟﻤﻌﻠﻮﻣﺎ ﻟﻮ ﻋﻠﻰ ﻟﺸﻜﻞ ﻋﺘﻤﺎ ﻋﻠﻰ ﻟﻤﻌﻠﻮﻣﺎ ﻟﻮ ﻓﻲ ﻹﻃﺎ ) ﻛﺘﺎ ﻟﺘﻠﻤﯿﺬ ( ﻧﺤﺼﻞ ﻋﻠﻰ ﺟﺪ
ﻟﺘﻨﺎﺳﺒﯿﺔ ﻵﻲﺗ
ﻗﯿﺲ ﻟﺰﯾﺔ ﻟﻲﺘ
ﺗﺤﺼﺮ ﻟﻘﻮ ) (
360 x
ﻃﻮ ﻟﻘﻮ ) cm ( p L 2 p r 2
ﯾﻨﺘﺞ ﻣﻦ ﺟﺪ ﻟﺘﻨﺎﺳﺒﯿﺔ
x 360
12
p
20
p
ﺣﻠﻮﻝ ﲤﺎﺭﻳﻦ ﺍﻟﻜﺘﺎﺏ ﺍﳌﺪﺭﺳﻲ ﺍﻟﺴﻨﺔ ﺍﻟﺜﺎﻟﺜﺔ ﻣﺘﻮﺳﻂ ﺩﺍﺭ ﻧﺰﻫﺔ ﺍﻷﻟﺒﺏﺎ

18
360
L
r
= 360
L
r


2
2
=
p
p


L
r
2
360 2
= x
ﻟﻌﻼﻗﺔ ﻟﺘﻲ ﺗﻌﻄﯿﻨﺎ ﻗﯿﺲ ﻟﺰﯾﺔ ﻟﻤﺮﻛﺰﯾﺔ ﻟﻘﻄﺎ ﻟﺴﻄﺢ ﻟﺠﺎﻧﺒﻲ ﻟﻤﺨﺮ ﻧﻲ ﻲ 360
L
r
= x
ﺣﯿﺚ r ﻮ ﻧﺼﻒ ﻗﻄﺮ ﻗﺮ ﻟﻘﺎﻋﺪ
L ﻮ ﻧﺼﻒ ﻗﻄﺮ ﻟﻘﻄﺎ ﻟﺬ ﯾﻤﺜﻞ ﻟﺴﻄﺢ ﻟﺠﺎﻧﺒﻲ ﻟﻠﻤﺨﺮ
ﺑﺈﺳﺘﻌﻤﺎ ﺬ ﻟﻌﻼﻗﺔ ﻟﺤﺴﺎ ﻗﯿﺲ ﻟﺰﯾﺔ ﻟﻤﺮﻛﺰﺔﯾ x ) ﻟﺴﺆ ) 2 (( ﻧﺤﺼﻞ ﻋﻠﻰ ﻧﻔﺲ ﻟﻨﺎﺗﺞ ﺑﺎﻟﻔﻌﻞ ﻟﺪﯾﻨﺎ
r = 6cm L = 10cm
210 = 6 36 =
10
6
360 = 360
L
r
= x
ﻧﺸﺎ ) 1 ( 194
1 ﻗﺒﻞ ﻟﺘﻄﺮ ﻟﻠﻔﺮ ﻷ ﻻ ﺑﺪ ﻣﻦ ﻟﺘﺄﻛﺪ ﻟﺘﻠﻤﯿﺬ ﻋﻠﻰ ﻋﻠﻢ ﺑﺄ ﺗﻔﺎ ﺮ ﻋﻤﻮ ﻋﻠﻰ ﻗﺎﻋﺪ ﺬ ﻟﮭﺮ ﯾﺸﻤﻞ ﮫﺳ
ﺣﺴﺎ ﻹﺗﻔﺎ ﻟﻤﺘﻌﻠﻖ ﺑﺎﻟﻘﺎﻋﺪ ] AB [ ﻓﻲ ﻟﻤﺜﺚﻠ ShB
ﯾﺮﺳﻢ ﻟﮭﺮ ﻋﻠﻰ ﻟﺴﺒﻮ ﯾﺒﺮ ﻟﻤﺜﺚﻠ SBh ﻣﺜﻼ
ﯾﺴﺘﻌﻤﻞ ﻣﺰ ﻟﺰﯾﺔﻟﻘﺎﺋﻤﺔ ﻋﻠﻰ ﻟﺸﻜﻞ ﺑﺎﻠﻟ ﻮ ﻷﺣﻤﺮ ﺛﻢ ﻧﺤﺴﺐ ﻹﺗﻔﺎ
ﺣﺴﺎ ﻟﻤﺴﺎﺣﺔ ﻟﺠﺎﻧﺒﯿﺔ ﻟﻠﮭﺮ ﻟﻤﻌﺘﺒﺮ
ﻋﻠﻰ ﻟﺘﻠﻤﯿﺬ ﻟﺘﻔﻄﻦ ﻟﻰ ﻟﻤﻌﻠﻮﻣﺔ ﻟﻮ ﻓﻲ ﻹﻃﺎ ) ﻛﺘﺎ ﻟﺘﻠﻤﯿﺬ (
2 ﯾﻄﻠﺐ ﻣﻦ ﻟﺘﻠﻤﯿﺬ ﯾﻮﺿﺢ ﻣﺎﻮ ﻟﻤﺮ ﺑﺎﻟﻤﺴﺎﺣﺔ ﻟﻜﻠﯿﺔ ﻟﻤﺠﺴﻢ ﺛﻢ ﻧﺤﺴﺐ ﻟﻤﺴﺎﺣﺔ ﻟﻤﻄﻠﻮﺑ ﺔ
ﻧﺸﺎ ) 2 ( 194
1 ﻣﺴﺎﺣﺔ ﺬ ﻟﻘﺮ
2
10 p = B ﻣﮫﻨ p 100 = B
2
360
10 360
10
5 . 4
2
p
= y ﻣﮫﻨ p 10 4.5 = y
ﺣﻠﻮﻝ ﲤﺎﺭﻳﻦ ﺍﻟﻜﺘﺎﺏ ﺍﳌﺪﺭﺳﻲ ﺍﻟﺴﻨﺔ ﺍﻟﺜﺎﻟﺜﺔ ﻣﺘﻮﺳﻂ ﺩﺍﺭ ﻧﺰﻫﺔ ﺍﻷﻟﺒﺏﺎ

19
ﻣﮫﻨ p 45 = y
3 ﻟﻤﺴﺎﺣﺔ ﻟﺠﺎﻧﺒﯿﺔ ﻟﻤﺨﺮ ﻟﺪ ﻟﻤﻌﯿ ﻦ ﻲ :
p 45 = y
ﻧﺸﺎ ) 3 ( 195
1 ﺑﻌﺪ ﺣﺴﺎ ﻃﻮ ﺣﺮ ﻟﮭﺮ ﺑﺈﺳﺘﻌﻤﺎ ﻧﻈﺮﯾﺔ ﻓﯿﺜﺎﻏﻮ
2 ﻧﺠﺎ ﺗﺼﻤﯿﻢ ﻟﻠﮭﺮ ﺑﺄﻛﺒﺮ ﻗﺔ ﻣﻤﻜﻨﺔ
3 ﺑﻌﺪ ﺻﻨﻊ ﻟﻤﻜﻌﺐ ﺑﺎﻟﻄﺮﯾﻘﺔ ﻟﻤﻄﻠﻮﺑﺔ ﯾﺴﺘﻨﺘﺞ ﻃﻮ ﺣﺮ ﻟﻤﻜﻌﺐ ﻟﻤﺼﻨﻮ ﻮ 8cm
4 ﻋﻠﻤﺎ ﻟﻤﻜﻌﺐ ﻧﺎﺗﺞ ﻋﻦ ﺗﺮﻛﯿﺐ 6 êﺮﻣﺎ
ﻟﮭﺎ ﻧﻔﺲ ﻷﺑﻌﺎ ﺳﻮ ﯾﺴﺘﻨﺘﺞ ﻟﺘﻠﻤﯿﺬ ﺣﺠﻢ ﻟﮭﺮ ﻮ :
ﺳﺪ ﺣﺠﻢ ﻟﻤﻜﻌﺐ ﻟﺬ ﺑﻌﺎ 8cm ,8cm , 8cm

3
cm
3
8
6
1
ﺑﻌﺪ ﻛﺘﺎﺑﺔ ﻟﻌﻼﻗﺔ ﻟﺘﻲ ﺗﺴﻤﺢ ﺑﺤﺴﺎ ﺬ ﻟﺤﺠﻢ ﺑﺎﻟﻜﯿﻔﯿﺔ ﻟﻤﻄﻠﻮﺑﺔ ) 8
2
1
( )
2
8 (
3
1
ﺣﯿﺚ
2
cm
2
8 ﻲ ﻣﺴﺎﺣﺔ ﻗﺎﻋﺪ ﻟﻤﻜﺐﻌ
8
2
1
ﻮ ﺗﻔﺎ ﻟﮭﺮ ﻮ ﯾﻀﺎ ﻧﺼﻒ ﺗﻔﺎ ﻟﻤﻜﺐﻌ
ﻧﺴﺘﻨﺘﺞ ﺣﺠﻢ ﻛﻞ ﺮ ﻣﻦ ﻷﺮﻣﺎ ﻟﺴﺘﺔ ﻮ
) ﺛﻠﺚ ﺟﺪ ﻣﺴﺎﺣﺔ ﻗﺎﻋﺪ ﻟﮭﺮ ﺗﻔﺎﻋﮫ (
5 ﻧﻄﻼﻗﺎ ﻣﻦ ﻛﻞ ﻣﺎ ﺳﺒﻖ ﻣﻦ ﻧﺠﺎ ﺻﻨﻊ ﺣﺴﺎ
ﺗﺴﺘﻨﺘﺞ ﻟﻘﺎﻋﺪ ﻟﻌﺎﻣﺔ ﻟﺤﺴﺎ ﺣﺠﻢ ﺮ ﻲ :
h B
3
1
= V ﺣﯿﺚ ﯾﺮﺰﻣ
B ﻟﻰ ﻣﺴﺎﺣﺔ ﻗﺎﻋﺪ ﻟﮭﺮ h ﻟﻰ ﺗﻔﺎ ﻟﮭﺮ
ﺣﻠﻮﻝ ﲤﺎﺭﻳﻦ ﺍﻟﻜﺘﺎﺏ ﺍﳌﺪﺭﺳﻲ ﺍﻟﺴﻨﺔ ﺍﻟﺜﺎﻟﺜﺔ ﻣﺘﻮﺳﻂ ﺩﺍﺭ ﻧﺰﻫﺔ ﺍﻷﻟﺒﺏﺎ

20
ﻧﺸﺎ ) 4 ( 196
ﻋﻠﻤﺎ ﻧﺼﻒ ﻗﻄﺮ ﻟﺪﺋﺮ ﻮ 2cm ﻓﺈ ﻣﺤﯿﻄﮭﺎ ﻮ
p 2 2 ﺣﻮﻟﻲ 12.56cm
ﻧﻼﺣﻆ ﻧﮫ ﻛﻠﻤﺎ ﻋﺪ ﺿﻼ ﻣﻨﺘﻈﻢ ﻛﻠﻤﺎ ﻛﺒﺮ ﻣﺤﯿﻄﮫ ﻗﺘﺮﺑﺖ ﻣﻦ ﻃﻮ ﻟﺪﺋﺮ ﻟﻤﺤﯿﻄﺔ ﺑﮫ 12.56cm
ﻛﻠﻤﺎ ﻛﺒﺮ ﻣﺴﺎﺣﺘﮫ ﻗﺘﺮﺑﺖ ﻣﻦ ﻣﺴﺎﺣﺔ ﻟﻘﺮ ﻟﻤﺤﺪ ﺑﮭﺬ ﻟﺪﺋﺮ
2
cm 12.566
ﻻﺣﻈﻨﺎ ﺿﻼ ﻟﻤﻀﻠﻌﺎ ﻟﻤﻨﺘﻈﺔﻤ ) 1 ( ) 2 ( ) 3 ( ) 4 ( ﻧﻘﺘﺮ ﺷﯿﺊ ﻓﺸﯿﺊ ﻣﻦ ﻣﺤﯿﻂ ﻟﻘﺮ
ﻣﻊ ﺗﻤﺎ ﺳﻢ ﻷﺮﻣﺎ ﻟﻤﻄﻠﻮﺑﺔ ﻧﻼﺣﻆ ﻟﺴﻄﺢ ﻟﺠﺎﻧﺒﻲ ﻟﮭﺬ ﻷﺮﻣﺎ ﯾﻘﺘﺮ ﺑﺪ ﻣﻦ ﺳﻄﺢ ﻣﻨﺤﻦ ﻣﻦ ﻟﺴﻄﺢ

ﻟﺠﺎﻧﺒﻲ ﻟﻤﺨﺮ ﻟﺪ
ﻣﻤﺎ ﺳﺒﻖ ﯾﻤﻜﻦ ﻧﺴﺘﻨﺘﺞ ﺣﺠﻢ ﻣﺨﺮ ﻟﺪ ﻮ
H B
3
1
= V
ﺣﯿﺚ ﯾﺮﺰﻣ B ﻟﻰ ﻣﺴﺎﺣﺔ ﻗﺮ ) ﻗﺎﻋﺪ ( ﻟﻤﺨﺮ h ﻟﻰ ﺗﻔﺎ ﺬ ﻟﻤﺨﺮ
ﺗﺠﺮﺑﺔ : ﯾﺴﺘﻨﺘﺞ ﻣﻦ ﺧﻼﻟﮭﺎ ﻗﺎﻋﺪ ﻟﺤﺴﺎ ﺣﺠﻢ ﻣﺨﺮ ﻟﺪ
ﻟﻨﺸﺎ ﯾﺘﻄﻠﺐ ﻣﻘﻮ ﻣﺴﺤﻮ ﻣﻠﺢ ﺳﻜﺮ ﻣﻞ
1 ﺻﻨﻊ ﺳﻄﻮﻧﺔ ﻟﺪ ﻣﺨﺮ ﻟﺪ ﻗﺎﻋﺪﺗﮭﻤﺎ ﻗﺮﺻﺎ ﻧﺼﻔﻲ ﻗﻄﺮﯾﮭﻤﺎ 3cm ﺗﻔﺎﻋﮭﻤﺎ 10cm ) ﯾﻠﻔﺖ ﻧﺘﺒﺎ
ﻟﺘﻠﻤﯿﺬ ﻟﻰ ﻗﺎﺑﻠﯿﺔ ﺗﻄﺎﺑﻖ ﻗﺎﻋﺪﺗﻲ ﻟﻤﺠﺴﻤﯿﻦ ﺗﺴﺎ ﺗﻔﺎﻋﯿﮭﺎﻤ
2 ﻣﻸ ﻣﺨﺮ ﻟﺪ ﺑﺎﻟﻤﺴﺤﻮ ﺣﺘﻰ ﻟﺤﺎﻓﺔ ﻟﻜﻦ ﺗﻜﺪﯾﺲ ﺛﻢ ﺳﻜﺐ ﻣﺤﺘﻮ ﻓﻲ ﻷﺳﻄﻮﺔﻧ
ﻛﺮ ﻟﻌﻤﻠﯿﺔ ﻋﺪ ﻣﻦ ﻟﻤﺮ ﻟﻼﻣﺔ ﺣﺘﻰ ﺗﻤﺘﻠﺊ ﻷﺳﻄﻮﺔﻧ
ﻣﺎﻮ ﻋﺪ ﻟﻤﺮ ﻟﺘﻲ ﻣﻸ ﻓﯿﮭﺎ ﻟﻤﺨﺮ ﻟﻜﻲ ﺗﻤﺘﻸ ﻷﺳﻄﻮﻧﺔ
ﺣﺴﺐ ﺣﺠﻢ ﻷﺳﻄﻮﻧﺔ ﺑﺄﺧﺬ ﻣﺤﺘﻮ ﻟﻤﺨﺮ ﻛﻮﺣﺪ ﻟﻠﻘﯿﺎ ﺛﻢ ﺑ
3
cm
ﺳﺘﻨﺘﺞ ﺣﺠﻢ ﻟﻤﺨﺮ ﺑﺪﻻﻟﺔ ﺣﺠﻢ ﻷﺳﻄﻮﻧﺔ ﺑ
3
cm
ﻧﻘﻞ ﻟﻨﺺ ﺛﻢ ﺗﻤﻤﮫ
ﻛﺎ ﻷﺳﻄﻮﻧﺔ ﻟﺪ ﻟﻤﺨﺮ ﻟﺪ ...........
ﺣﻠﻮﻝ ﲤﺎﺭﻳﻦ ﺍﻟﻜﺘﺎﺏ ﺍﳌﺪﺭﺳﻲ ﺍﻟﺴﻨﺔ ﺍﻟﺜﺎﻟﺜﺔ ﻣﺘﻮﺳﻂ ﺩﺍﺭ ﻧﺰﻫﺔ ﺍﻷﻟﺒﺏﺎ

21
ﻗﺎﺑﻠﺘﺎ ﻟﻠﻤﻄﺎﺑﻘﺔ ﺎﻛ ﻟﮭﻤﺎ ﻧﻔﺲ .......... ﻓﺈ :
ﺣﺠﻢ ﻣﺨﺮ ﻟﺪ ﯾﺴﺎ ........ ﺣﺠﻢ ﺳﻄﻮﻧﺔ ﻟﺪ .
ﺑﻌﺪ ﺬ ﯾﺴﺘﻨﺘﺞ ﻟﻘﺎﻋﺪ :
ﻛﺎﺖﻧ B ﻲ ﻣﺴﺎﺣﺔ ﻟﻘﺎﻋﺪﺗﯿﻦ ﻛﺎ h ﻹﺗﻔﺎ ﻟﻤﺸﺘﺮ ﻟﮭﺬﯾﻦ ﻟﻤﺠﺴﻤﯿﻦ ﻓﺈ : h B ....... = ....

iman31
  • : Mar 2015
  • : oran
  • : 29
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iman31
03-31-2015

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