Transcript
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    Chuyn Hnh hc 11 - thyTrn Vit Knh Quan hsong song

    Hocmai.vnNgi trng chung ca hc tr Vit Tng i t vn: 1900 58-58-12 - Trang | 1 -

    I. Chng minh ba im M, N, P thng hng:

    + Tm trong hnh v hai mt phng khc nhau: mp (ABC), mp (ABC) cha M, N, P.

    + Chng minh: M, N, P ( )ABC

    M, N, P ( ' ' ') A B C

    Theo tin TNG GIAO suy ra ( ) ( ' ' ') ABC A B C ng thng t i qua M, N, P M, N, P

    thng hng.

    II. Tm giao tuyn hai mt phng (P) v mp (Q) cho trc:

    + Tm trong hnh vhai im A, B nm trn mp (P) v mp (Q) (c chng minh).

    + S dng tin Tng giao ( ) ( )mp P mp Q Dt AB

    II. Tm giao im ca ng thng v mt phng (P):

    + Chn trong hnh v mt phng (Q) cha d.

    Tm giao tuyn ( ) ( )t mp P mp Q

    + Tm : ( )( )

    M d M d t Cm M d P

    M P

    Gio vin : Trn Vit Knh

    Ngun : Hocmai.vn

    BI 02.

    CC DNG TON C BN

    TI LIU BI GING

    http://hocmai.vn/http://hocmai.vn/http://hocmai.vn/
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    Chuyn Hnh hc 11 - ThyTrn Vit Knh Quan hsong song

    Hocmai.vnNgi trng chung ca hc tr Vit Tng i t vn: 1900 58-58-12 - Trang | 1 -

    Bi 1:Cho hnh bnh hnh ABCD . S l im khng thuc (ABCD) ,M v N ln lt l trung im ca

    on AB v SC.

    a. Xc nh giao im I = AN (SBD)

    b. Xc nh giao im J = MN (SBD)

    c. Chng minh I , J , B thng hng

    Bi 2:

    Cho t din SABC.Gi L, M, N ln lt l cc im trn cc cnh SA, SB v AC sao cho LM

    khng song song vi AB, LN khng song song vi SC.

    a. Tm giao tuyn ca mp (LMN) v (ABC)

    b. Tm giao im I = BC ( LMN) v J = SC ( LMN)

    c. Chng minh M , I , J thng hng.

    Bi 3:

    Cho bn imA ,B ,C , D khng cng nm trong mt mt phng.

    a. Chng minhAB v CD cho nhau

    b. Trn cc on thng AB v CD ln lt ly cc imM, Nsao cho ng thngMNct ng

    thngBD tiI. Hi imI thuc nhng mt phng no? X giao tuyn ca hai mp (CMN) v ( BCD)

    Bi 4. Cho t dinABCD ,M l mt im bn trong tam gicABD , N l mt im bn trong tam

    gicACD . Tm giao tuyn ca cc cp mt phng sau:

    a. (AMN) v (BCD)

    b. (DMN) v (ABC )

    Bi 5: Cho t gic ABCD v S (ABCD). Gi M , N l hai im trn BC v SD.a. Tm giao im I = BN ( SAC)

    b. Tm giao im J = MN ( SAC)

    c. Chng minh C , I , J thng hng

    Ngun : Hocmai.vn

    BI GING 02.

    CC DNG TON C BN

    BI T P T LUY N

    http://hocmai.vn/http://hocmai.vn/http://hocmai.vn/
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    Chuyn Hnh hc 11 - ThyTrn Vit Knh Quan h song song

    Hocmai.vn Ngi trng chung ca hc tr Vit Tng i t vn: 1900 58-58-12 - Trang | 1 -

    Bi 1:Cho hnh bnh hnh ABCD . S l im khng thuc (ABCD) ,M v N ln lt l trung im caon AB v SC .a. Xc nh giao im I = AN (SBD)

    b. Xc nh giao im J = MN (SBD)c. Chng minh I , J , B thng hng

    Gii:

    a. Xc nh giao im I = AN (SBD ) Chn mp ph (SAC) AN Tm giao tuyn ca (SAC ) v (SBD)

    ( SAC) (SBD) = SO Trong (SAC), gi I = AN SO

    I ANI SO m SO ( SBD) I ( SBD)

    Vy: I = AN ( SBD)b. Xc nh giao im J = MN (SBD) Chn mp ph (SMC) MN

    Tm giao tuyn ca (SMC ) v (SBD)S l im chung ca (SMC ) v (SBD)Trong (ABCD) , gi E = MC BD ( SAC) (SBD) = SE

    Trong (SMC), gi J = MN SEJMNJ SE m SE ( SBD) J ( SBD)

    Vy J = MN ( SBD)c. Chng minh I , J , B thng hngTa c : B l im chung ca (ANB) v ( SBD)

    I SO m SO ( SBD) I ( SBD) I AN m AN (ANB) I (ANB)

    I l im chung ca (ANB) v ( SBD) J SE m SE ( SBD) J ( SBD)

    BI GING 02.

    CC DNG TON C BN

    P N BI T P T LUY N

    IJ

    E

    A

    BC

    M

    ND

    S

    O

    J

    E

    I

    O

    S

    C

    N

    M B

    A

    D

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    Chuyn Hnh hc 11 - ThyTrn Vit Knh Quan h song song

    Hocmai.vn Ngi trng chung ca hc tr Vit Tng i t vn: 1900 58-58-12 - Trang | 2 -

    J MN m MN (ANB) J (ANB) J l im chung ca (ANB) v ( SBD)

    Vy : B , I , J thng hngBi 2:Cho t din SABC.Gi L, M, N ln lt l cc im trn cc cnh SA, SB v AC sao cho LMkhng song song vi AB, LN khng song song vi SC.a. Tm giao tuyn ca mp (LMN) v (ABC)

    b. Tm giao im I = BC ( LMN) v J = SC ( LMN)c. Chng minh M , I , J thng hng.

    Gii:a. Tm giao tuyn ca mp (LMN) v (ABC)Ta c : N l im chung ca (LMN) v (ABC)Trong (SAB) , LM khng song song vi AB

    Gi K = AB LMK LM m LM (LMN ) K (LMN )K AB m AB ( ABC) K ( ABC)

    b. Tm giao im I = BC ( LMN) Chn mp ph (ABC) BC Tm giao tuyn ca (ABC ) v (LMN)

    (ABC) ( LMN) = NK Trong (ABC), gi I = NK BC

    I BCI NK m NK (LMN ) I (LMN)

    Vy : I = BC ( LMN)Tm giao im J = SC ( LMN) Trong (SAC), LN khng song song vi SC

    Gi J = LN SC

    J SCJ LN m LN (LMN ) J (LMN)

    Vy : J = SC ( LMN)c. Chng minh M , I , J thng hngTa c : M , I , J l im chung ca (LMN) v ( SBC)Vy : M , I , J thng hng

    Bi 3:Cho bn imA ,B ,C , D khng cng nm trong mt mt phng.a. Chng minhAB v CD cho nhau

    b. Trn cc on thng AB v CD ln lt ly cc im M, Nsao cho ng thng MNct ng

    thngBD tiI. Hi imI thuc nhng mt phng no? X giao tuyn ca hai mp (CMN) v ( BCD)

    Gii :a. Chng minh AB v CD cho nhau :Gi sAB v CD khng cho nhauDo c mp () chaAB v CDA ,B ,C , D nm trong mp () mu thun gi thuytVy : AB v CD cho nhaub. im I thuc nhng mp : I MN m MN(ABD ) I (ABD ) I MN m MN(CMN ) I (CMN ) I BD m BD (BCD ) I (BCD )X giao tuyn ca hai mp (CMN) v ( BCD) l CI

    K

    JI

    S

    C

    M

    L

    N

    B

    A

    M

    I

    C

    B D

    N

    A

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    Chuyn Hnh hc 11 - ThyTrn Vit Knh Quan h song song

    Hocmai.vn Ngi trng chung ca hc tr Vit Tng i t vn: 1900 58-58-12 - Trang | 3 -

    Bi 4.Cho t dinABCD , M l mt im bn trong tam gicABD , N l mt im bn trong tamgicACD . Tm giao tuyn ca cc cp mt phng sau:a. (AMN) v (BCD)

    b. (DMN) v (ABC )Gii :

    a. Tm giao tuyn ca (AMN) v (BCD)Trong (ABD ) , gi E = AMBD

    EAM m AM ( AMN) E ( AMN)EBD m BD ( BCD) E ( BCD)

    E l im chung ca mp ( AMN) v (BCD )Trong (ACD ) , gi F = ANCD

    FAN m AN ( AMN) F ( AMN)FCD m CD ( BCD) F ( BCD)

    Fl im chung ca mp ( AMN) v (BCD )Vy:EFl giao tuyn ca mp ( AMN) v (BCD )

    b. Tm giao tuyn ca (DMN) v (ABC)Trong (ABD ) , gi P = DMAB

    PDM m DM ( DMN) P (DMN )PAB m AB ( ABC) P (ABC)

    P l im chung ca mp ( DMN) v (ABC )Trong (ACD) , gi Q = DNAC

    Q DN m DN ( DMN) Q ( DMN)Q AC m AC( ABC) Q ( ABCA)

    Q l im chung ca mp ( DMN) v (ABC )Vy:PQ l giao tuyn ca mp ( DMN) v (ABC )

    Bi 5.Cho t gic ABCD v S (ABCD). Gi M , N l hai im trn BC v SD.a. Tm giao im I = BN ( SAC)

    b. Tm giao im J = MN ( SAC)c. Chng minh C , I , J thng hng

    Giia. Tm giao im I = BN ( SAC) Chn mp ph (SBD) BN Tm giao tuyn ca (SBD ) v (SAC)

    Trong (ABCD), gi O = AC BD (SBD) ( SAC) = SO

    Trong (SBD), gi I = BN SOI BN

    B

    C

    ED

    F

    N

    M

    Q

    P

    A

    O

    J

    K

    I

    M

    N

    A

    D

    CB

    S

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    Chuyn Hnh hc 11 - ThyTrn Vit Knh Quan h song song

    Hocmai.vn Ngi trng chung ca hc tr Vit Tng i t vn: 1900 58-58-12 - Trang | 4 -

    I SO m SO (SAC ) I (SAC)Vy : I = BN ( SAC)b. Tm giao im J = MN ( SAC) : Chn mp ph (SMD) MN Tm giao tuyn ca (SMD ) v (SAC)

    Trong (ABCD), gi K = AC DM

    (SMD) ( SAC) = SK Trong (SMD), gi J = MN SK

    J MNJ SK m SK (SAC ) J (SAC)

    Vy : J = MN ( SAC)c. Chng minh C , I , J thng hng:Ta c : C , I , J l im chung ca (BCN ) v (SAC)Vy : C , I , J thng hng

    Ngun : Hocmai.vn


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