Parallelogram vs Trapezoid
Parallelogram thiab trapezoid (lossis trapezium) yog ob lub ntsej muag quadrilaterals. Txawm hais tias cov no yog quadrangles, lub geometry ntawm lub trapezoid txawv ntawm cov parallelograms.
Parallelogram
Parallelogram tuaj yeem txhais tau tias yog daim duab geometric nrog plaub sab, nrog rau sab nraud sib npaug rau ib leeg. Ntau precisely nws yog quadrilateral nrog ob khub ntawm parallel sab. Qhov xwm txheej sib npaug no muab ntau yam geometric yam ntxwv rau cov parallelograms.
Ib plaub plaub yog ib qho parallelogram yog tias pom cov yam ntxwv geometric.
• Ob khub ntawm kev tawm tsam yog sib npaug ntawm qhov ntev. (AB=DC, AD=BC)
• Ob khub ntawm lub kaum sab xis sib npaug. ([latex]D\hat{A}B=B\hat{C}D, A\hat{D}C=A\hat{B}C[/latex])
• Yog cov ces kaum uas nyob ib sab yog supplementary [latex]D\hat{A}B + A\hat{D}C=A\hat{D}C + B\hat{C}D=B\hat {C}D + A\hat{B}C=A\hat{B}C + D\hat{A}B=180^{circ}=\pi rad[/latex]
• Ib khub ntawm sab, uas tawm tsam ib leeg, yog sib npaug thiab sib npaug ntawm qhov ntev. (AB=DC & AB∥DC)
• Diagonals bisect ib leeg (AO=OC, BO=OD)
• Txhua kab kab pheeb ces kaum faib cov plaub fab rau hauv ob daim duab peb sab congruent. (∆ADB ≡ ∆BCD, ∆ABC ≡ ∆ADC)
Ntxiv mus, qhov sib npaug ntawm cov squares ntawm ob sab yog sib npaug rau cov lej ntawm cov squares ntawm kab pheeb ces kaum. Qhov no qee zaum hu ua txoj cai parallelogram thiab muaj kev siv dav hauv physics thiab engineering. (AB2 + BC2 + CD2 + DA2=AC2 + BD2)
Txhua tus yam ntxwv saum toj no tuaj yeem siv los ua cov khoom, thaum nws tau tsim tias lub plaub fab yog ib qho parallelogram.
Thaj tsam ntawm parallelogram tuaj yeem suav los ntawm cov khoom ntawm qhov ntev ntawm ib sab thiab qhov siab mus rau sab nraud. Yog li ntawd, thaj tsam ntawm parallelogram tuaj yeem teev tau raws li
Area of parallelogram=base × × h
Thaj tsam ntawm parallelogram yog ywj siab ntawm cov duab ntawm tus kheej parallelogram. Nws tsuas yog nyob ntawm qhov ntev ntawm lub hauv paus thiab qhov siab perpendicular.
Yog hais tias ob sab ntawm lub parallelogram tuaj yeem sawv cev los ntawm ob lub vectors, thaj chaw tuaj yeem tau txais los ntawm qhov loj ntawm cov khoom vector (khoom khoom hla) ntawm ob lub vectors uas nyob ib sab.
Yog ob sab AB thiab AD yog sawv cev los ntawm vectors ([latex]\overrightarrow{AB}[/latex]) thiab ([latex]\overrightarrow{AD}[/latex]) feem, thaj tsam ntawm parallelogram muab los ntawm [latex]\left | \overrightarrow{AB}\times \overrightarrow{AD} right |=AB\cdot AD \sin \alpha [/latex], where α is the angle between [latex]\overrightarrow{AB}[/latex] and [latex]\overrightarrow{AD}[/latex].
Ua raws li yog qee cov khoom siab tshaj ntawm cov parallelogram;
• Thaj chaw ntawm ib qho parallelogram yog ob npaug ntawm thaj tsam ntawm daim duab peb sab tsim los ntawm ib qho ntawm nws kab pheeb ces kaum.
• Cheeb tsam ntawm qhov parallelogram muab faib ua ib nrab los ntawm ib kab twg dhau los ntawm qhov nruab nrab.
• Ib qho kev hloov pauv uas tsis yog degenerate affine yuav siv lub parallelogram mus rau lwm parallelogram
• Ib qho parallelogram muaj symmetry rotational symmetry 2
• Cov lej ntawm qhov kev ncua deb ntawm txhua qhov taw qhia sab hauv ntawm lub parallelogram rau ob sab yog ywj siab ntawm qhov chaw ntawm qhov taw tes
Trapezoid
Trapezoid (los yog Trapezium hauv Askiv Askiv) yog lub ntsej muag quadrilateral uas tsawg kawg yog ob sab sib npaug thiab tsis sib npaug ntawm qhov ntev. Ob sab ntawm lub trapezoid yog lub hauv paus thiab ob sab yog hu ua ob txhais ceg.
Ua raws li cov yam ntxwv tseem ceeb ntawm trapezoids;
• Yog tias cov ces kaum uas nyob ib sab tsis nyob ntawm tib lub hauv paus ntawm lub trapezoid, lawv yog cov ces kaum ntxiv. i.e. lawv ntxiv mus txog 180° ([latex]B\hat{A}D+A\hat{D}C=A\hat{B}C+B\hat{C}D=180^{circ}[/latex])
• Ob kab pheeb ces kaum ntawm lub trapezium sib tshuam ntawm tib qhov sib piv (qhov sib piv ntawm ntu ntawm kab pheeb ces kaum sib npaug).
• Yog tias a thiab b yog hauv paus thiab c, d yog ob txhais ceg, qhov ntev ntawm kab pheeb ces kaum yog muab los ntawm
[latex]\sqrt{frac{ab^{2}-a^{2}b-ac^{2}+bd^{2}}{b-a}}[/latex]
thiab
[latex]\sqrt{frac{ab^{2}-a^{2}b-ac^{2}+bc^{2}}{b-a}}[/latex]
Thaj tsam ntawm lub trapezoid tuaj yeem suav nrog siv cov qauv hauv qab no
Area of trapezoid=[latex]\frac{a+b}{2}\times h[/latex]
Qhov txawv ntawm Parallelogram thiab Trapezoid (Trapezium) yog dab tsi?
• Ob qho tib si parallelogram thiab trapezoid yog convex quadrilaterals.
• Nyob rau hauv ib qho parallelogram, ob khub ntawm cov tawm tsam yog sib npaug thaum, nyob rau hauv lub trapezoid, tsuas yog ib khub yog parallel.
• Cov kab pheeb ces kaum ntawm qhov parallelogram bisect ib leeg (1: 1 ratio) thaum cov kab pheeb ces kaum ntawm lub trapezoid sib tshuam nrog qhov sib piv tsis tu ncua ntawm ntu.
• Thaj chaw ntawm lub parallelogram nyob ntawm qhov siab thiab lub hauv paus thaum thaj tsam ntawm lub trapezoid nyob ntawm qhov siab thiab nruab nrab ntu.
• Ob daim duab peb sab uas tsim los ntawm kab pheeb ces kaum nyob rau hauv ib qho parallelogram yeej ib txwm sib haum thaum cov duab peb sab ntawm lub trapezoid tuaj yeem sib xyaw lossis tsis tau.
