I-SCHOOL247 ingathanda ukwazisa ku Isihloko: I-lemma ye-trapezoidal kanye nomugqa ofanayo we-Math 8. Lo mbhalo uhlanganiselwe ukwethula abafundi ekuzilolongeni kokuzifundela kanye nokubuyekeza ulwazi lohlelo lwezibalo. Ngethemba ukuthi lokhu kuzoba inkomba ewusizo ohlelweni lwakho lokufunda.
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Izihloko zokukhuthaza i-HSG
I-trapezoidal lemma kanye nokumakwa komgwaqo kwe-Dong Fund
I. Ulwazi lokukhumbula
1) I-Trapezoidal Lemma
“Ku-trapezoid enezisekelo ezimbili ezingalingani, umugqa odlula empambanweni yama-diagonals futhi unqamula imigqa equkethe izinhlangothi ezimbili udlula phakathi nendawo yezisekelo ezimbili.”
Fakazela:
Ukuphambana kwe-AB, i-CD mayibe ngu-H, ye-AC, BD ibe ngu-G, i-midpoint ka-AD, BC ibe ngu-E kanye no-F
Ukujoyina i-EG, FG, sine: (Delta)ADG (sim) (Delta)CBG (gg) , ngakho :
(fractextADtextCB=fractextAGtextCGRightarrow fractext2AE{text 2CF=fractextAG{textCGRightarrow fractextAEtextCF=fractextAG umbhaloCG) (1)
Siphinde sibe: (widehattextEAG=widehattextFCG) (SL in ) (2)
Kusukela ku-(1) kanye no-(2) thola : (Delta )AEG (sim) (Delta )CFG (cgc)
Ngakho: (widehattextAGE=widehattextCGFRightarrow ) E , G , H qondanisa (3)
Ngokufanayo, sinalokhu: (Delta )AEH (sim) (Delta )BFH(Rightarrow widehattextAHE=widehattextBHF )
(Umcibisholo) H , E , F qondanisa (4)
Kusukela ku-(3) kanye no-(4) infer: H , E , G , F collinear
2) I-beam yomugqa ofanayo
Uma imigqa efanayo inqamula imigqa emibili ehambisanayo, bese ichaza kuleyo migqa emibili ehambisanayo amasegimenti emigqa ehambisanayo.
Uma u-m// n, imigqa emithathu ethi a, b, c ngesikhathi esisodwa kokuthi O inqamula m kokuthi A, B, C bese isika n kokuthi A’, B’, C’ bese
(fractextABtextA !!’!!umbhalo B !!’!!umbhalo umbhalo = fractextBCtextB !!’!!umbhalo C !!’!!text =fractext ACumbhaloA !!’!!umbhalo C !!’!!umbhalo ) noma (frac{textAB textBCtext = fractextA !!’!!umbhalo B !!’!!umbhalo umbhaloB !!’!!umbhalo C !!’!!umbhalo umbhalo ; fractextABtext AC=fractextA !!’!!umbhalo B !!’!!umbhalo umbhaloA ! !’!!umbhalo C !!’!!umbhalo )
*Hlehla:
+ Uma imigqa emithathu lapho emibili iphambana khona futhi ichazwa emigqeni emibili ehambisanayo enamapheya alinganiselayo amasegimenti omugqa, leyo migqa emithathu iyafana.
+ Uma imigqa emibili iphambana ngemigqa emithathu efanayo ukuze yakhe amapheya amasegimenti omugqa ahambisana ngokulinganayo, khona-ke ayahambisana.
II. Ukuzivocavoca
1. Ukuzivocavoca kwe-eseyi
Isifundo 1:
I-ABCD mayibe yi-quadrilateral, lapho u-M eyindawo emaphakathi ye-CD kanye no-N emaphakathi ne-CB. Ukwazi AM, AN usike i-BD ibe izingxenye ezintathu ezilinganayo. Fakazela ukuthi i-ABCD iyipharalelogram
Umklomelo
Vumela u-E, F kube ukuphambana kwe-AM, AN nge-BD; I-G, H iyimpambanondlela ye-MN ene-AD, BD
I-MN // BC (MN isilinganiso ezihambayo se-(Delta)BCD)
(Rightarrow ) I-Quadrilateral HBFM iyi-trapezoid enezinhlangothi ezimbili ezivumelana ku-A, N iyindawo emaphakathi yesisekelo se-BF, ngakho ngokusho kwe-trapezoidal lemma, u-N umaphakathi we-MH ephansi.
(Umcibisholo )MN = NH (1)
Ngokufanayo: ku-CDEN ye-trapezoid, u-M uyindawo emaphakathi ye-GN (Rightarrow ) GM = MN (2)
Kusukela ku-(1) kanye (2) ne-infer GM = MN = OKUNCANE
Sine (Delta)BNH = (Delta)CNM (cgc) (Rightarrow ) (widehattextBHNtext = widehattextCMN ) (I-Rightarrow ) bảo hành // cm noma AB // CD (a)
Okufanayo: (Delta )GDM = (Delta)NCM (cgc) (Rightarrow ) (widehattextDGMtext = widehattextCNM ) (I-Rightarrow ) GD // công nhân noma AD // CB (b)
Kusukela ku-(a) kanye no-(b) kulandela ukuthi i-ABCD ye-quadrilateral inamapheya ezinhlangothi eziphambene ezihambisanayo, ngakho iyipharalelogramu.
Isifundo 2:
Vumela (Delta)I-ABC ibe nama-engeli amathathu abukhali, i-orthocenter H, umugqa odlula ku-H unqamule u-AB no-AC, ngokulandelana, kokuthi P, Q kangangokuthi HP = HQ. Makube u-M phakathi nendawo ka-BC. Ubufakazi: HM $bot $PQ
Umklomelo
Ukuphambana kwemigwaqo kuka-AH no-BC makube ngu-I
Kusuka ku-C draw cn // PQ (N(in) AB),
Sifakazela i-MH (bot)CN (Rightarrow ) HM (bot )PQ
I-quadrilateral CNPQ iyi-trapezoid, H iyindawo emaphakathi ye-PQ, izinhlangothi ezimbili ze-NP ne-CQ zihambisana ku-A, ngakho-ke u-K umaphakathi we-CN (Rightarrow ) MK isilinganiso sokuthi (Delta) BCN (Umcibisholo ) MK // cn (Umcibisholo wangakwesokudla ) MK // AB (1)
U-H uyisikhungo se-orthocenter se-(Delta)ABC ngakho-ke CH (bot ) AB (2)
Kusukela ku-(1) kanye no-(2) kulandela ukuthi i-MK (bot )CH (Rightarrow ) MK iwubude be-(Delta)CHK (3)
Kusukela ku-AH (bot )BC (Umcibisholo) MC(bot )HK (Rightarrow ) ngươi wubude be-(Delta)CHK (4)
Kusukela ku-(3) kanye no-(4) kulandela ukuthi u-M uyi-orthocenter ye-(Delta)CHK(Rightarrow ) MH(bot )CN (Rightarrow ) MH(bot ) I-PQ
………
—(Okuqukethwe okugcwele, izimpendulo ezinemininingwane yemibuzo yokuhlolwa, sicela ubone ku-inthanethi noma ungene ngemvume ukuze uzilande)—
2. Izivivinyo zokukhetha eziningi
Isifundo 1: Khetha umusho ofanele emishweni elandelayo:
A. I-trapezoid inama-engeli amathathu a-obtuse kanye ne-acute angle.
B. I-trapezoid inama-engeli amathathu angakwesokudla kanye ne-engeli eyodwa e-acute.
C. I-trapezoid inama-engeli amathathu abukhali kanye ne-engeli eyodwa ye-obtuse.
D. Ibha inama-engeli a-acute okungenani amabili futhi okungenani ama-engeli amabili a-obtuse.
Isixazululo somhlahlandlela
Isamba sama-engeli e-trapezoid singama-360.0.
+ I-trapezoid inama-engeli amathathu a-obtuse kanye ne-engeli ebukhali.
Isibonelo: I-trapezoid inama-engeli ama-obtuse angu-3 angu-100.0,12001350 futhi i-acute angle ingu-600.
⇒ Isamba sama-engeli ama-4 we-trapezoid siyi-1000 + 1200 + 1350 + 600 = 4150 > 3600
⇒ Ayikho i-trapezoid enama-engeli amathathu a-obtuse kanye ne-acute angle eyodwa. ⇒ Impendulo A ayilungile
I-trapezoid inama-engeli amathathu angakwesokudla kanye ne-engeli eyodwa ye-acute.
Isibonelo: I-trapezoid inama-engeli angu-3 alingana no-90.0 kanye ne-acute angle engu-650.
⇒ Isamba sama-engeli angu-4 e-trapezoid singama-900 + 900 + 900 + 650 = 3350 0
⇒ Ayikho i-trapezoid enama-engeli amathathu angakwesokudla kanye ne-acute angle eyodwa. ⇒ Impendulo B ayilungile.
+ I-trapezoid inama-engeli amathathu abukhali kanye ne-engeli eyodwa ye-obtuse.
Isibonelo: I-trapezoid inama-engeli amathathu abukhali we-45.0750,800i-engeli eyi-obtuse ingu-1600
⇒ Isamba sama-engeli angu-4 e-trapezoid singama-450 +750 + 800 + 1600 = 3600
⇒ Ukuba khona kweTrapezoid kunama-engeli amathathu ashubile, i-engeli eyodwa eyi-obtuse. ⇒ Impendulo C ilungile
⇒ I-trapezoid inama-engeli a-acute okungenani ama-3. ⇒ Impendulo D ayilungile.
Khetha impendulo C.
Isifundo 2: I-trapezoid inama-engeli aphikisanayo angu-125.0 futhi 750elinye ipheya lama-engeli aphambene we-trapezoid lithi ?
A. 1050,550
B. 1050450
C. 1150,550
D. 1150650
Isixazululo somhlahlandlela
Isamba sama-engeli amane e-trapezoid singama-3600.
Cabanga ukuthi sinama-engeli aphikisanayo angu-1250 futhi 750
⇒ Isamba sezilinganiso zamanye amapheya amabili ama-engeli aphikisanayo siyi-1600.
Uma sicabangela impendulo, sinepheya ye-1050,550 anelise.
Khetha impendulo A.
Isifundo 3: I-Trapezoid ABCD ine IKHOFI + KULULA = 1500. Bese A + SUSA = ?
A. 2200
B. 2100
C. 2000
D. 1900
Isixazululo somhlahlandlela
Isamba sama-engeli amane e-trapezoid singama-3600.
Bese sine: A + SUSA + IKHOFI + KULULA = 3600 ⇒ A + SUSA = 3600 – ( IKHOFI + KULULA )
⇒ A + SUSA = 3600 – 1500 = 2100.
Khetha impendulo B.
Isifundo 4: Vumela i-ABCD ibe yi-trapezoid lapho A = 1200, SUSA = 600, KULULA = 1350 bese kuba isilinganiso se-engeli IKHOFI = ?
A. 550
B. 450
C. 500
D. 600
Isixazululo somhlahlandlela
Isamba sama-engeli amane e-trapezoid singama-3600.
Bese sine: A + SUSA + IKHOFI + KULULA = 3600 ⇒ IKHOFI = 3600 – ( A + SUSA + KULULA )
⇒ IKHOFI = 3600 – ( 1200 + 600 + 1350 = 450.
Khetha impendulo B.
Into 5: I-ABCD mayibe yi-trapezoid yesikwele, isikwele ku-A no-D. Vumela i-AD = 3 centimet ne-CD = 4 centimet. Bala i-AC?
A. 3cm
B. 4cm
C. 3.5cm
D. 5cm
Isixazululo somhlahlandlela
Njengoba i-quadrilateral ABCD iyi-trapezoid ebheke kwesokudla, KULULA = 90o
Ngakho, unxantathu i-ADC ingunxantathu ongakwesokudla ku-D.
Ukusebenzisa i-theorem ye-Pythagorean kunxantathu wesokudla i-ACD sine:
AC2 = AD2 + DC2 = 322 + 42 = 25
I-Infer: AC = 5cm
Khetha impendulo ELULA
Isifundo 6: I-ABCD mayibe yi-quadrilateral eyi-convex ene-AB // CD kanye ne-AD = 6cm; I-DC = 8cm ne-AC = 10cm. Thola isitatimende esingamanga?
I-A. Triangle ADC ine-engeli yesokudla kokuthi D.
B. I-Quadrilateral ABCD iyi-trapezoid
C. I-Quadrilateral ABCD iyi-trapezoid ebheke kwesokudla ene KULULA = 90o
D. I-Quadrilateral ABCD iyi-trapezoid eyisikwele ene SUSA = 90o
Isixazululo somhlahlandlela
I-Quadrilateral ABCD ine-AB // CD, ngakho-ke i-ABCD ye-quadrilateral iyi-trapezoid enezisekelo ezi-2 u-AB ne-CD.
Cabangela unxantathu we-ACD nge: AD2 + I-CD2 = AC2 (6)2 + 82 = 102 = 100)
I-Infer: unxantathu i-ADC ingunxantathu ongakwesokudla ku-D.
Ngakho-ke: KULULA = 90o
I-Infer: I-Quadrilateral ABCD iyi-trapezoid ebheke kwesokudla ene KULULA = 90o
Ngakho, isitatimende D singamanga
Khetha impendulo ELULA
………
—(Okuqukethwe okugcwele, izimpendulo ezinemininingwane yemibuzo yokuhlolwa, sicela ubone ku-inthanethi noma ungene ngemvume ukuze uzilande)—
Okungenhla kuyingxenye yokuqukethwe kwedokhumenti Isihloko: I-lemma ye-trapezoidal kanye nomugqa ofanayo we-Math 8. Ukuze ubone izinkomba eziwusizo, ungakhetha ukubuka ku-inthanethi noma ungene ngemvume ku-hoc247.net ukuze udawunilode amadokhumenti kukhompuyutha yakho.
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