Geometry yog kev tshawb fawb ntawm cov duab thiab cov ces kaum. Kev kawm cov txuj ci no yuav zoo li nyuaj rau ntau tus tub ntxhais kawm. Muaj ntau lub ntsiab lus uas yog qhov tshiab hauv geometry thiab lawv tuaj yeem txaus ntshai rau cov tub ntxhais kawm. Koj yuav tsum kawm postulates, cov ntsiab lus, thiab cov cim kom nkag siab txog geometry. Yog tias koj ua ke coj tus cwj pwm kawm zoo thiab ob peb lub tswv yim ntawm geometry, koj tuaj yeem txawj ua geometry.
Kauj ruam
Ntu 1 ntawm 3: Tau Qhab Nia
Kauj Ruam 1. Mus koom txhua chav kawm
Chav Kawm yog qhov chaw kawm paub yam tshiab thiab txhawb cov ntaub ntawv uas koj yuav tau kawm hauv cov chav kawm dhau los. Yog tias koj tsis mus koom chav kawm, koj yuav pom tias nws nyuaj rau khaws cov ntaub ntawv tshiab kawg.
- Nug hauv chav kawm. Koj tus kws qhia ntawv yuav tsum xyuas kom tseeb tias koj nkag siab cov ntaub ntawv uas tau qhia lawm. Yog koj muaj lus nug, tsis txhob ua siab deb nug lawv. Qee tus ntawm lwm tus tub ntxhais kawm hauv chav kawm yuav muaj lus nug ib yam li koj.
- Ua ntej nkag mus hauv chav kawm, nyeem cov ntaub ntawv uas yuav tsum tau qhia thiab cim cov qauv, cov lus pom, thiab kev tshaj tawm.
- Saib koj tus kws qhia ntawv hauv chav kawm. Tham nrog koj cov phooj ywg tsuas yog thaum so lossis tom qab kawm ntawv.
Kauj Ruam 2. Kos daim duab
Geometry yog kev ua lej ntawm cov duab thiab cov ces kaum. Txhawm rau nkag siab geometry, nws yuav yooj yim dua yog tias koj pom qhov teeb meem thiab kos duab kos. Yog koj raug nug txog lub kaum sab xis, kos nws. Kev sib raug zoo ntawm cov ces kaum yuav yooj yim pom hauv daim duab. Yog tias tsis muaj daim duab, kos nws.
- Nkag siab txog cov yam ntxwv ntawm cov duab thiab pom lawv yog cov khoom tseem ceeb ntawm kev ua haujlwm geometry.
- Xyaum lees paub cov duab hauv ntau yam kev taw qhia thiab raws li lawv cov yam ntxwv geometric (ntsuas lub kaum ntse ntse, tus naj npawb ntawm txoj kab thiab kab sib dhos, thiab lwm yam)
Kauj Ruam 3. Tsim pawg kawm
Pawg kawm yog ib txoj hauv kev zoo los kawm cov ntaub ntawv thiab qhia cov ntsiab lus uas koj tsis nkag siab. Muaj cov pab pawg tshawb fawb uas tau ntsib tas li yuav yuam kom koj nyeem thiab nkag siab cov ntaub ntawv tam sim no. Kev kawm nrog cov phooj ywg hauv chav kawm tuaj yeem muaj txiaj ntsig thaum koj tab tom daws teeb meem nyuaj dua. Koj tuaj yeem kawm thiab nkag siab nws ua ke.
Ib tus ntawm koj cov phooj ywg tuaj yeem nkag siab cov khoom koj tsis nkag siab thiab tuaj yeem pab koj. Koj kuj tseem tuaj yeem pab koj tus phooj ywg nkag siab qee yam thiab thaum kawg ua tus tswv cov ntaub ntawv zoo dua thaum qhia lawv
Kauj Ruam 4. Paub yuav siv tus kws tiv thaiv dab tsi
Tus protractor yog cov cuab yeej siv ib nrab siv los ntsuas cov ces kaum. Cov cuab yeej no tseem tuaj yeem siv los kos cov ces kaum. Paub paub siv tus kws tiv thaiv kom raug yog qhov txuj ci tseem ceeb hauv kev kawm geometry. Txhawm rau ntsuas qhov loj ntawm lub kaum sab xis:
- Muab qhov chaw nruab nrab ntawm tus kws tiv thaiv txoj cai rau ntawm lub kaum sab xis ntawm lub ces kaum.
- Tig tus protractor kom txog thaum kab hauv qab yog ncaj qha saum ib ntawm ob txhais ceg tsim lub kaum sab xis.
- Ntev lwm ceg tag nrho txoj kev mus rau sab saum toj ntawm tus kws txiav txim plaub ntug thiab nco ntsoov qib uas lub kaum sab ceg poob. Qhov no yog qhov tshwm sim ntawm kev ntsuas lub kaum sab xis.
Kauj Ruam 5. Ua txhua txoj haujlwm thiab ua tom tsev
Kev ua homework yog siv los pab koj nkag siab txhua lub ntsiab lus hauv cov khoom. Ua homework yuav ua rau koj paub txog cov ntsiab lus uas koj twb nkag siab thiab cov ncauj lus twg koj xav paub ntau ntxiv txog.
Yog tias koj pom nws nyuaj rau nkag siab qee cov ncauj lus hauv kev sib raug zoo nrog pej xeem, mloog zoo rau cov ncauj lus ntawd kom txog thaum koj nkag siab tiag. Nug koj tus phooj ywg hauv chav kawm lossis tus kws qhia ntawv kom tau txais kev pab
Kauj Ruam 6. Qhia cov ntaub ntawv
Thaum koj nkag siab lub ntsiab lus lossis lub tswv yim tiag tiag, koj yuav tsum muaj peev xwm piav qhia rau lwm tus. Yog tias koj tsis tuaj yeem piav qhia nws txog thaum lwm tus neeg nkag siab, muaj feem yuav koj tsis nkag siab nws ib yam. Qhia lwm tus neeg cov ntaub ntawv tseem yog ib txoj hauv kev zoo los ua kom koj nco tau ntau dua.
- Sim qhia koj cov nus muag lossis niam txiv txog geometry.
- Mus tom ntej thiab piav qhia cov ntsiab lus uas koj nkag siab tiag tiag thaum kawm hauv pab pawg.
Kauj Ruam 7. Ua cov lus nug xyaum
Mastering geometry xav tau kev paub thiab txuj ci. Kev kawm cov cai ntawm geometry yam tsis ua teeb meem xyaum tsis txaus kom tau txais A. Koj yuav tsum ua koj cov ntawv hauv tsev thiab xyaum ua cov lus nug txog cov ntsiab lus uas koj tsis nkag siab.
- Nco ntsoov tias koj ua ntau cov lus nug xyaum ua tau los ntawm ntau qhov chaw. Cov lus nug zoo ib yam tuaj yeem nthuav tawm hauv ntau txoj hauv kev thiab tej zaum yuav yooj yim rau koj nkag siab.
- Qhov teeb meem ntau ntxiv uas koj ua haujlwm, nws yuav yooj yim dua rau koj los daws lawv tom ntej.
Kauj Ruam 8. Thov kev pab ntxiv
Qee zaum mus rau hauv chav kawm thiab tham nrog tus kws qhia ntawv tsis txaus. Koj yuav xav tau tus kws qhia ntawv uas tuaj yeem siv sijhawm rau cov ncauj lus uas nyuaj rau koj nkag siab. Kawm nrog ib tus neeg tus kheej tuaj yeem muaj txiaj ntsig zoo rau kev nkag siab cov khoom nyuaj.
- Nug koj tus kws qhia yog tias muaj cov kws qhia muaj nyob hauv tsev kawm ntawv.
- Koom nrog cov kev qhia qhia ntxiv los ntawm koj tus kws qhia ntawv thiab nug koj cov lus nug hauv chav kawm.
Ntu 2 ntawm 3: Kawm Lub Tswv Yim Geometry
Kauj Ruam 1. Kawm Euclid's Tsib Postulates ntawm Geometry
Geometry yog ua raws tsib txoj haujlwm ua los ntawm cov lej lej qub, Euclid. Paub thiab nkag siab txog tsib nqe lus no yuav pab koj kawm ntau yam tswv yim hauv geometry.
- 1: Ib txoj kab ncaj tuaj yeem rub txuas ob qho ntsiab lus.
- 2: Txhua txoj kab ncaj tuaj yeem txuas ntxiv mus tas li hauv ib qho kev taw qhia.
- 3. Lub voj voos tuaj yeem kos ib ncig ntawm kab nrog ib lub ntsiab lus ua haujlwm nruab nrab thiab qhov ntev ntawm kab raws li lub vojvoog ntawm lub voj voog.
- 4. Txhua txoj cai kaum yog sib haum
- 5. Yog tias muaj kab thiab kab lus taw tes, tsuas yog ib txoj kab tuaj yeem hla hla lub ntsiab lus ntawd thiab txuas mus rau thawj kab.
Kauj Ruam 2. Txheeb xyuas cov cim uas siv hauv cov teeb meem geometry
Thaum koj tab tom kawm thawj zaug, ntau lub cim tuaj yeem ua rau tsis meej pem. Kawm lub ntsiab lus ntawm txhua lub cim thiab tuaj yeem lees paub nws sai yuav ua rau txoj kev kawm yooj yim dua. Hauv qab no yog qee cov cim uas nquag siv hauv geometry:
- Daim duab peb sab me me sawv cev rau daim duab peb sab.
- Lub ces kaum me me piav qhia tus yam ntxwv ntawm lub ces kaum.
- Ib kab ntawm cov tsiaj ntawv uas muaj kab nyob saum lawv sawv cev rau tus yam ntxwv ntawm kab kab.
- Kab ntawv ntawm kab ntawv nrog kab cim nrog tus xub saum toj no nws piav qhia cov yam ntxwv ntawm kab.
- Ib txoj kab kab nrog kab ntsug nyob hauv nruab nrab txhais tau tias ob kab sib tshuam ib leeg.
- Ob txoj kab ntsug txhais tau tias ib kab sib dhos rau lwm txoj kab.
- Qhov sib npaug kos npe ntxiv rau kab squiggly saum nws txhais tau tias ob lub dav hlau tsis sib haum.
- Ib txoj kab me ntsis txhais tau tias ob daim duab yuav luag zoo ib yam.
- Peb lub ntsiab lus uas ua ib daim duab peb sab txhais tau tias "yog li ntawd".
Kauj Ruam 3. Nkag siab txog cov yam ntxwv ntawm kab
Ib txoj kab ncaj tuaj yeem txuas ntxiv infinity hauv ob qho kev qhia. Ib kab kos nrog tus cim xub thaum kawg txhais tau tias kab tuaj yeem txuas ntxiv mus tas li. Kab ib kab muaj qhov pib thiab xaus qhov chaw. Lwm daim ntawv hu ua kab hluav taws xob: nws tsuas tuaj yeem txuas rau hauv ib qho kev taw qhia. Cov kab tuaj yeem muab tso ua ke, sib npaug, lossis sib tshuam.
- Ob kab sib dhos rau ib leeg tsis tuaj yeem sib tshuam.
- Ob txoj kab sib dhos tsim lub kaum sab xis ntawm 90 °.
- Txoj kab hla yog ob kab uas sib tshuam ua ke. Cov kab sib tshuam yuav tsum yog kab rov tav, tab sis tsis tuaj yeem ua ke.
Kauj Ruam 4. Paub ntau hom kaum
Muaj peb hom kaum: obtuse, mob, thiab perpendicular. Lub kaum obtuse yog lub kaum sab xis uas siab dua 90 °; Lub kaum ntse ntse yog lub kaum sab xis uas tsawg dua 90 °, thiab lub kaum sab xis ib sab yog lub kaum sab xis uas ntsuas 90 °. Muaj peev xwm txheeb xyuas cov ces kaum yog ib yam tseem ceeb hauv kev kawm geometry.
Lub kaum sab xis ntawm 90 ° yog lub kaum sab xis: ob kab tsim lub kaum ntse ntse zoo meej
Kauj Ruam 5. Nkag Siab Pythagorean Theorem
Pythagorean Theorem hais2 + b2 = c2. Nov yog cov lej uas suav qhov ntev ntawm qhov hypotenuse ntawm daim duab peb sab yog tias koj twb paub qhov ntev ntawm ob sab lawm. Txoj cai daim duab peb sab yog daim duab peb sab uas ib lub kaum sab xis yog 90 ° zoo meej. Hauv theorem, a thiab b yog qhov sib thooj ib leeg thiab yog ib sab ntawm daim duab peb sab, thaum c yog hypotenuse ntawm daim duab peb sab.
- Piv txwv: Xam qhov ntev ntawm hypotenuse ntawm daim duab peb sab yog tias a = 2 thiab b = 3.
- a2 + b2 = c2
- 22 + 32 = c2
- 4 + 9 = c2
- 13 = c ib2
- c = 13 hli
- c = 3,6
Kauj Ruam 6. Xib fwb qhia paub seb hom twg peb tog
Muaj peb hom duab peb sab: kev xav, isosceles, thiab sib npaug. Tsis muaj ntawm peb sab ntawm daim duab peb sab yog qhov ntev tib yam. Ib daim duab peb sab isosceles muaj ob sab sib npaug thiab ob lub kaum sib npaug. Ib daim duab peb sab muaj peb sab sib npaug thiab peb lub kaum sib npaug. Los ntawm kev paub txog hom duab peb sab, koj tuaj yeem txheeb xyuas cov yam ntxwv thiab kev cuam tshuam nrog txhua daim duab peb sab.
- Nco ntsoov, daim duab peb sab sib npaug kuj tseem tuaj yeem hu ua isosceles triangle vim nws muaj ob sab uas zoo ib yam nkaus. Txhua daim duab peb sab sib npaug yog daim duab peb sab isosceles, tab sis tsis yog txhua daim isosceles triangles yog daim duab peb sab
- Cov duab peb sab kuj tseem tuaj yeem ua pawg raws qhov loj ntawm cov ces kaum: mob hnyav, raug, thiab obtuse. Ib daim duab peb sab muaj lub kaum sab xis tsawg dua 90 °; daim duab peb sab obtuse muaj lub kaum sab xis ntau dua 90 °.
Kauj Ruam 7. Paub qhov sib txawv ntawm qhov zoo sib xws thiab sib haum (zoo sib xws thiab sib haum)
Cov duab zoo sib xws yog cov duab uas muaj cov ces kaum zoo ib yam, tab sis nws sab qhov ntev sib piv me dua lossis loj dua. Hauv lwm lo lus, polygons muaj tib lub kaum ntse ntse tab sis txawv sab ntev. Cov duab sib xws txhais tau tias zoo ib yam thiab sib xws; Cov duab no muaj tib lub kaum sab xis thiab sab ntev.
Cov piv txwv sib piv yog cov ces kaum uas muaj qhov sib npaug sib npaug hauv ob daim duab. Hauv daim duab peb sab xis, cov ces kaum ntawm 90 degrees hauv ob daim duab peb sab yog qhov sib npaug. Txhawm rau kom muaj cov ces kaum sib piv, cov duab tsis tas yuav muaj tib sab loj
Kauj Ruam 8. Kawm paub ntxiv thiab ntxiv cov ces kaum
Cov ces kaum ntxiv yog cov kaum uas ntxiv txog 90 degrees, thaum cov ces kaum ntxiv mus txog 180 degrees. Nco ntsoov tias cov ces kaum yeej ib txwm sib haum; cov ces kaum sab hauv thiab cov ces kaum sab nrauv uas tsis sib thooj yog ib txwm sib haum. Lub kaum sab xis yog 90 degrees, thaum txoj kab ncaj ncaj muaj lub kaum sab xis ntawm 180 degrees.
- Lub kaum sab xis ntsug yog ob lub kaum sab xis tsim los ntawm ob txoj kab sib tshuam.
- Cov ces kaum sab hauv yog tsim thaum ob kab sib tshuam los ntawm kab thib peb. Cov ces kaum nyob ntawm ob sab ntawm kab thib peb; ntawm sab hauv (sab hauv) ntawm kab thawj thiab thib ob.
- Cov ces kaum sab nrauv kuj tau tsim thaum ob kab sib tshuam nrog kab thib peb. Cov ces kaum nyob ntawm ob sab ntawm kab thib peb; tab sis nyob sab nrauv (sab nrauv) ntawm kab thib ib thiab thib ob.
Kauj Ruam 9. Nco ntsoov RING-FIRE-VILLAGE
RING-FIRE-VILLAGE yog cov cuab yeej zoo uas tuaj yeem pab koj nco qab cov qauv rau sine, cosine, thiab tangent ntawm daim duab peb sab. Thaum koj yuav xam cov sine, cosine, thiab tangent, siv cov qauv hauv qab no. Sine = TEEB MEEM/SIRING (lub nplhaib), Cosine = SIDE/SIDE (lim), Tangen = TUAJ LAWM/SIRING (lub zos).
- Piv txwv: Xam lub sine, cosine, thiab tangent ntawm lub kaum sab xis 39 ° ntawm txoj cai peb tog nrog sab ntev AB = 3, BC = 5 thiab AC = 4.
- sin (39 °) = rau pem hauv ntej/skew = 3/5 = 0, 6
- cos (39 °) = sab/nqes hav = 4/5 = 0, 8
- tan (39 °) = pem hauv ntej/sab = 3/4 = 0.75
Ntu 3 ntawm 3: Sau 2 Kab Ntawv Pov Thawj
Kauj Ruam 1. Kos daim duab tom qab nyeem qhov teeb meem
Qee zaum teeb meem geometry raug muab yam tsis muaj duab thiab koj yuav tsum kos daim duab kom pom qhov pov thawj. Tom qab koj tau kos duab ntxhib uas haum rau qhov teeb meem, koj yuav tsum rov sau daim duab kom koj tuaj yeem nyeem cov ntsiab lus kom meej thiab cov ces kaum uas koj tab tom ua yog ntau dua lossis tsawg dua.
- Xyuas kom koj sau daim ntawv kom meej raws li cov ntaub ntawv muab.
- Qhov pom tseeb ntawm daim duab koj ua, nws yooj yim dua rau koj los daws qhov teeb meem.
Kauj Ruam 2. Saib daim duab uas koj tau tsim
Daim ntawv lo rau lub kaum sab xis thiab ob sab sib npaug. Yog tias ib kab txuas mus rau lwm qhov, sau daim ntawv lo piav qhia nws. Yog tias qhov teeb meem tsis tau hais meej meej tias ob kab sib npaug, koj puas tuaj yeem ua pov thawj tias ob kab yog qhov sib npaug? Nco ntsoov tias koj tuaj yeem ua pov thawj txhua qhov kev xav uas koj siv.
- Sau cov kev sib raug zoo ntawm cov kab thiab cov ces kaum uas koj tuaj yeem xaus raws li koj daim duab thiab kev xav.
- Sau tag nrho cov lus qhia hauv qhov teeb meem. Hauv kev pov thawj geometry, yuav muaj qee cov ntaub ntawv muab los ntawm qhov teeb meem. Sau tag nrho cov lus qhia muab los ntawm qhov teeb meem yuav pab koj ua tiav cov ntawv pov thawj.
Kauj Ruam 3. Ua haujlwm rov qab rau pem hauv ntej
Thaum koj sim ua pov thawj qee yam hauv geometry, koj yuav tau txais ob peb nqe lus hais txog cov duab thiab cov ces kaum, tom qab ntawd koj yuav tsum ua pov thawj vim li cas cov lus ntawd muaj tseeb. Qee zaum, txoj hauv kev yooj yim tshaj plaws los ua qhov no yog pib qhov kawg ntawm qhov teeb meem.
- Cov lus nug yuav xaus qhov no li cas?
- Puas muaj cov kauj ruam meej uas koj yuav tsum ua pov thawj kom mus txog qhov kev txiav txim siab ntawd?
Kauj Ruam 4. Tsim kom muaj ob kab ntawv kab ntawv sau tias "Nqe lus" thiab "Vim Li Cas"
Txhawm rau kom tau txais pov thawj zoo, koj yuav tsum tau tshaj tawm thiab muab cov laj thawj geometric uas ua pov thawj cov lus tseeb. Hauv qab kab lus sau, sau ib nqe lus xws li kaum sab xis ABC = kaum sab xis DEF. Hauv kab ntawv vim li cas, sau cov pov thawj uas txhawb nqa nqe lus. Yog tias qhov laj thawj tau muab los ua cov ntsiab lus rau lo lus nug, sau 'muab los ntawm lo lus nug'. Yog tsis yog, sau cov theorem uas ua pov thawj cov lus.
Kauj Ruam 5. Txiav txim siab seb cov theorem twg tsim nyog los ua pov thawj
Muaj ntau qhov theorems hauv geometry uas koj tuaj yeem siv ua pov thawj. Ntau tus yam ntxwv peb tog, sib tshuam thiab kab sib luag, thiab cov voj voos tau siv los ua lub hauv paus rau cov theorems no. Txiav txim seb yam duab geometric uas koj tab tom ua thiab nrhiav cov duab uas tuaj yeem siv tau hauv cov txheej txheem pov thawj. Txheeb xyuas cov pov thawj yav dhau los txhawm rau txheeb xyuas qhov zoo sib xws. Kab lus no tsis tuaj yeem sau tag nrho cov theorems geometric, tab sis hauv qab no yog qee qhov tseem ceeb tshaj plaws ntawm daim duab peb sab theorems:
- Ob lossis ntau daim duab peb sab sib xws yuav muaj qhov ntev sib xws thiab cov ces kaum sib xws. Hauv Lus Askiv, cov txheej txheem no luv dua rau CPCTC (Qhov sib thooj ntawm Cov Duab Peb Hlis Sib Xws yog Sib Haum).
- Yog tias qhov ntev ntawm peb sab ntawm ib daim duab peb sab sib npaug rau qhov ntev ntawm peb sab ntawm lwm daim duab peb sab, ob daim duab peb sab yog sib haum. Hauv Askiv, theorem no hu ua SSS (side-side-side).
- Ob daim duab peb sab yog sib haum yog tias lawv muaj ob sab uas zoo ib yam ntev thiab ib lub kaum sab xis uas zoo ib yam. Hauv Askiv, qhov theorem no hu ua SAS (side-angle-side).
- Ob daim duab peb sab yog sib haum yog tias lawv muaj ob lub kaum sib npaug sib npaug thiab ib sab uas zoo ib yam nkaus. Hauv Askiv, qhov theorem no hu ua ASA (angle-side-angle).
- Yog tias ob lossis ntau daim duab peb sab muaj tib lub kaum ntse ntse, nws txhais tau tias daim duab peb sab zoo ib yam, tab sis tsis tas yuav tsum sib haum. Hauv Askiv, qhov theorem no hu ua AAA (angle-angle-angle).
Kauj Ruam 6. Ua kom ntseeg tau tias koj ua raws cov kauj ruam uas tsim nyog
Sau ib daim duab qhia ntawm koj qhov pov thawj. Sau txhua qhov laj thawj tom qab txhua kauj ruam. Ntxiv cov lus nug hauv cov kauj ruam uas cuam tshuam rau cov lus qhia. Tsis txhob sau tag nrho cov lus qhia thaum pib ntawm qhov pov thawj. Rov teem dua cov ntawv pov thawj yog tias tsim nyog.
Qhov pov thawj ntau koj ua, nws yuav yooj yim dua rau koj los teeb tsa cov ntawv pov thawj kom raug
Kauj Ruam 7. Sau qhov xaus ntawm kab kawg
Kauj ruam kawg yuav tsum ua kom tiav koj cov ntawv pov thawj, tab sis cov kauj ruam kawg no tseem xav tau qhov ua pov thawj. Tom qab koj ua tiav cov ntawv pov thawj, rov nyeem nws thiab paub tseeb tias tsis muaj qhov hauv koj qhov kev xav. Thaum koj paub tseeb tias koj cov ntaub ntawv pov thawj raug, sau QED hauv qab kaum sab xis txhawm rau hais meej tias koj cov ntawv pov thawj tiav.
Lub tswv yim
- Kawm Txhua Hnub. Rov nyeem cov ntawv niaj hnub no, sau ntawv nag hmo, thiab cov ntaub ntawv uas koj tau kawm yav dhau los yog li koj tsis txhob hnov qab cov lus pom/theorems, cov ntsiab lus lossis cov cim/cim.
- Nyeem cov vev xaib thiab vis dis aus txog cov ntsiab lus uas koj tsis nkag siab.
- Npaj cov ntawv nyeem nrog cov qauv los pab koj nco thiab rov nyeem dua.
- Nug tus lej xov tooj thiab email chaw nyob ntawm qee tus phooj ywg hauv koj chav kawm geometry kom lawv tuaj yeem pab thaum koj kawm tom tsev.
- Kawm cov chav kawm nyob rau lub semester luv dhau los yog li koj tsis tas yuav ua haujlwm hnyav nyob rau xyoo kawm ntawv ib txwm muaj.
- Ua kev xav. Qhov no tuaj yeem pab koj.
Ceeb toom
- Tsis txhob ncua sijhawm
- Tsis txhob sim kawm txhua yam ntaub ntawv hauv lub sijhawm luv
