Tom qab nyeem cov ntaub ntawv, tus nyeem ntawv yuav nkag siab tias cov phiaj xwm tsis nyuaj. Kab lus muab cov lus qhia tseem ceeb tshaj plaws thiab cov qauv tsim nyog rau kev daws teeb meem tshwj xeeb. Cov nqe lus tseem ceeb thiab cov khoom ntawm cov duab tau muab tso rau ntawm lub txee.
Definition and tseem ceeb facts
Planimetry yog ib ceg ntawm geometry uas txiav txim siab cov khoom ntawm lub tiaj ob sab. Qee qhov piv txwv tsim nyog tuaj yeem txheeb pom: square, voj voog, rhombus.
Ntawm lwm yam, nws tsim nyog hais txog qhov taw tes thiab kab. Lawv yog ob lub ntsiab lus tseem ceeb ntawm cov phiaj xwm.
Txhua yam yog twb ua rau lawv, piv txwv li:
- Ib ntu yog ib feem ntawm txoj kab ncaj nraim los ntawm ob lub ntsiab lus.
- Ray yog ib yam khoom zoo ib yam li ntu, txawm li cas los xij, muaj ciam teb ntawm ib sab nkaus xwb.
- Ib lub kaum sab xis uas muaj ob lub rays tawm ntawm tib lub ntsiab lus.
Axioms and theorems
Cia peb mus saib ze rau ntawm axioms. Hauv Planimetry, cov no yog cov cai tseem ceeb tshaj plaws uas txhua qhov kev tshawb fawb ua haujlwm. Yog, thiab tsis tsuas yog nyob rau hauv nws. Los ntawmlos ntawm kev txhais, cov no yog cov lus uas tsis xav tau pov thawj.
Cov axioms uas yuav tau tham hauv qab no yog ib feem ntawm qhov hu ua Euclidean geometry.
- Muaj ob lub ntsiab lus. Ib kab ib txwm tuaj yeem kos los ntawm lawv.
- Yog ib kab muaj, ces muaj cov ntsiab lus uas dag rau nws thiab cov ntsiab lus uas tsis dag rau nws.
2 nqe lus no hu ua axioms of membership, and the following ones are order:
- Yog tias muaj peb lub ntsiab lus ntawm txoj kab ncaj nraim, ces ib ntawm lawv yuav tsum nyob nruab nrab ntawm ob.
- Ib dav hlau muab faib los ntawm ib txoj kab ncaj nraim rau hauv ob feem. Thaum qhov kawg ntawm ntu nyob ntawm ib nrab, ces tag nrho cov khoom belongs rau nws. Txwv tsis pub, thawj kab thiab ntu muaj qhov sib tshuam.
Axioms of Measures:
- Txhua ntu muaj qhov ntev uas tsis yog xoom. Yog hais tias lub ntsiab lus tawg nws mus rau ntau qhov chaw, ces lawv cov lej yuav sib npaug rau qhov ntev ntawm qhov khoom.
- Txhua lub kaum sab xis muaj qee qhov ntsuas, uas tsis sib npaug rau xoom. Yog hais tias koj faib nws nrog ib tug nqaj, ces lub kaum sab xis pib yuav muab sib npaug rau cov sum ntawm cov tsim sawv daws yuav.
Parallel:
Muaj kab ncaj nraim ntawm lub dav hlau. Los ntawm ib qho taw tes uas tsis yog nws, tsuas yog ib txoj kab ncaj nraim tuaj yeem kos mus rau qhov muab
Theorems hauv planimetry tsis yog cov lus tseem ceeb ntxiv lawm. Lawv feem ntau lees txais qhov tseeb, tab sis txhua tus ntawm lawv muaj cov pov thawj tsim los ntawm cov ntsiab lus tseem ceeb uas tau hais los saum no. Tsis tas li ntawd, muaj ntau ntawm lawv. Nws yuav nyuaj heev rau disassemble txhua yam, tab sis cov khoom uas nthuav tawm yuav muaj qee yamntawm lawv.
Ob lub hauv qab no tsim nyog kuaj xyuas ntxov:
- Cov sum ntawm cov ces kaum uas nyob ib sab yog 180 degrees.
- Vertical angles muaj nqi tib yam.
Ob lub theorems no tuaj yeem siv tau los daws cov teeb meem geometric ntsig txog n-gons. Lawv yog cov yooj yim heev thiab intuitive. Tsim nyog nco txog lawv.
Tsib 3
Daim duab peb sab yog daim duab geometric uas muaj peb ntu txuas txuas ntxiv. Lawv raug cais raws li ob peb yam.
Nyob rau sab (kev faib tawm los ntawm cov npe):
- Equilateral.
- Isosceles - ob sab thiab cov ces kaum sib npaug sib npaug.
- Versatile.
Ntawm cov ces kaum:
- ncig-angled;
- rectangular;
- obtuse.
Ob lub ces kaum yuav ntse tsis hais qhov xwm txheej twg, thiab qhov thib peb yog txiav txim los ntawm thawj ntu ntawm lo lus. Ntawd yog, daim duab peb sab txoj cai muaj ib lub kaum sib npaug li 90 degrees.
Properties:
- Lub kaum sab loj dua, qhov loj dua sab nraud.
- Cov sum ntawm tag nrho cov ces kaum yog 180 degrees.
- Thaj chaw tuaj yeem suav nrog tus qauv: S=½ ⋅ h ⋅ a, qhov twg a yog sab, h yog qhov siab kos rau nws.
- Koj tuaj yeem sau ib lub voj voog hauv daim duab peb sab lossis piav qhia ib puag ncig nws.
Ib qho ntawm cov qauv ntawm cov phiaj xwm phiaj xwm yog Pythagorean theorem. Nws ua haujlwm tshwj xeeb rau daim duab peb sab thiab suab zoo li no: squarelub hypotenuse yog sib npaug zos rau cov sum ntawm cov squares ntawm ob txhais ceg: AB2 =AC2 + BC2.
Lub hypotenuse yog sab opposite rau lub kaum sab xis 90 °, thiab ob txhais ceg yog nyob ib sab.
Quadagons
Muaj lus qhia ntau txog qhov no. Hauv qab no tsuas yog cov tseem ceeb tshaj plaws.
Qee yam:
- Parallelogram - cov sab nraud yog sib npaug thiab sib npaug hauv cov khub.
- Rhombus yog parallelogram uas nws ob sab yog tib qhov ntev.
- Rectangle - parallelogram nrog plaub lub kaum sab xis
- Ib lub square yog ob lub rhombus thiab ib daim duab plaub.
- Trapezium - tsuas yog ob sab rov qab ua ke.
Properties:
- Cov lej ntawm sab hauv yog 360 degrees.
- Thaj chaw ib txwm suav nrog siv tus qauv: S=√(p-a)(p-b)(p-c)(p-d), qhov twg p yog ib nrab ntawm ib puag ncig, a, b, c, d yog ob sab ntawm duab.
- Yog tias lub voj voog tuaj yeem piav qhia nyob ib puag ncig plaub, ces kuv hu nws convex, yog tias tsis yog - tsis yog convex.
