Chidziwitso chokwanira komanso chatsatanetsatane cha geometry ya giredi 4

1. Kudziwa kukumbukira

1. Rectangle: Rectangle ndi quadrilateral yokhala ndi ngodya zinayi zakumanja, 2 m’mbali mwake molingana ndi mbali ziwiri zazifupi zofanana ndi .

Perimeter: 𝑷 = (𝒂 + 𝒃) × 𝟐 (mulingo womwewo).

Chigawo: 𝑺 = 𝒂 × 𝒃 (mulingo womwewo).

Chenjerani:

– Sikweya ndi rectangle yapadera (yokhala ndi mbali zinayi zofanana).

Kuzungulira kwa rectangle ndi nambala yomwe imagawidwa ndi 2 ngati kutalika ndi m’lifupi ndi manambala achilengedwe.

– Ngati kutalika kwa rectangle kuchulukitsidwa ndi unit, kuzungulira kumawonjezera nkhwangwa ndi mayunitsi awiri (chifukwa pali 2 kutalika)

– Ngati kukula kwa rectangle kuchulukitsidwa ndi gawo, kuzungulira kumawonjezera nkhwangwa ndi mayunitsi awiri (chifukwa pali 2 wides)

– Ngati kutalika kwa rectangle kuchepetsedwa ndi unit, perimeter imatsika ndi nkhwangwa ndi ma unit 2 (chifukwa pali 2 kutalika)

– Ngati m’lifupi mwa rectangle wachepetsedwa ndi gawo, kuzungulira kumatsika ndi nkhwangwa ndi mayunitsi awiri (chifukwa pali 2 wides)

– Mukachulukitsa gawo limodzi la rectangle, malowo adzawonjezeka kangati.

– Mukachepetsa gawo limodzi la rectangle nthawi zambiri, malowo amachepera nthawi zambiri.

– Ngati miyeso yonse ikukwera kapena kuchepa, malowo amachulukitsa kapena kuchepetsa zomwe zidapangidwa nthawi ziwirizo.

2. Square: Sikweya ndi quadrilateral yokhala ndi ngodya zinayi zakumanja ndi mbali zinayi zofanana

Perimeter: = × (mulingo womwewo)

Chigawo: 𝑺 = 𝒂 × 𝒂 (mulingo womwewo).

Chenjerani:

– Mu lalikulu, ngati mbali imodzi ichulukitsidwa ndi gawo, kuzungulira kumawonjezeka ndi mayunitsi 4.

Mu lalikulu, ngati mbali ionjezedwa kangapo, malowo amachulukitsa nkhwangwa.

– Perimeter ya sikweya ndi nambala yomwe imatha kugawidwa ndi 4 ngati mbali ya sikweya ndi nambala yachilengedwe.

3. Parallelogram: Paralelogalamu ndi quadrilateral yokhala ndi mapeyala awiri a mbali zopingana ndi ofanana ndi .

Paralelogalamu yokhala ndi ngodya yolondola ndi nkhani yapadera ya rectangle.

Chigawo: 𝑺 = 𝒂 × 𝒉 (mulingo womwewo).

4. Rhombus: Rombus ndi quadrilateral yokhala ndi mbali ziwiri zofanana ndi mbali zinayi zofanana

Chigawo: = 1/2 (m x n ) (mulingo womwewo).

2. Mitundu ya masewera olimbitsa thupi

Fomu 1: Masamu pa kuzindikira zithunzi

Mitundu iwiri yodziwika bwino ndi iyi:

• Mtundu 1: Werengani mayina a mawonekedwe omwe apezeka pa chithunzi choperekedwa.

Gulu ili silovuta koma nthawi zambiri amalakwitsa kulemba mndandanda wazithunzi zomwe zikusowa kapena zobwereza. Kuti tigonjetse, tiyenera kuwerenga mwadongosolo lasayansi, monga:

– Werengani zigawo zonse za mzere monga momwe zimafunira chifukwa cha vuto kuti mawonekedwewa ali ndi vertex yofanana motsatizana mpaka ma vertices onse otsala atha.

– Zithunzi za ana zimagawidwa pazithunzi zomwe tapatsidwa, ifenso timalemba mwana aliyense ndi nambala 1; 2; 3; … Werengani mayina azithunzi molingana ndi zofunikira za mutu womwe uli ndi zithunzi zokhala ndi nambala imodzi (1 chithunzi cha mwana) chikhoza kukhala, pitilizani kuwerenga mayina azithunzi ndi zithunzi za ana 2 ndiye zithunzi za ana 3 ndi zina zotero…

Powerenga, zindikirani kuti ziwerengero zobwerezabwereza zimawerengedwa kamodzi kokha.

• Mtundu 2: Werengani kuchuluka kwa mawonekedwe omwe apezeka ngati chithunzi cham’mbuyocho chili ndi ma vertices ambiri (mfundo), ambiri. Tiyenera kuchita izi munjira ziwiri:

– Khwerero 1: Kuwerengera kuchuluka kwa ziwerengero zomwe zapezedwa molingana ndi zofunikira za nkhani yosavuta (ganizirani zingapo zingapo).

– Khwerero 2: Pezani lamulo la kuchuluka kwa mawonekedwe (kutengera lamulo la kutsatizana kwa manambala). Kuchokera pamenepo, kutengera malamulo ndi njira zowerengera.

Zochita zowonetsera

Phunziro 1: Potengera chithunzi chomwe chili pansipa: Chithunzicho chili ndi m’mphepete 8, kulumikiza ma vertices awiri omwe sali m’mphepete momwemo kudzapeza diagonal. Ndi ma diagonal angati?

Yankho:

Njira 1: Chithunzicho chili ndi ma vertices 8, kotero pali njira 8 zosankhira mfundo yoyamba, mutasankha mfundo yoyamba, tili ndi ma vertices 7, kotero pali njira 7 zosankha mfundo yachiwiri kuti mugwirizane ndi mfundo yoyamba kuti mupeze mzere wowongoka. .

Njira iliyonse yosankha timapeza 1 mzere woterewu ndi 7 × 8 = 56 mizere, koma kotero mzere uliwonse wawerengedwa kawiri, kotero chiwerengero chenicheni cha zigawo za mzere ndi 56: 2 = 28 mizere.

Popeza chiwerengerocho chili ndi mbali 8, chiwerengero cha diagonal mu chithunzi ndi: 28 – 8 = 20 (diagonals).

Njira 2: Kupyolera mu vertex iliyonse ya chithunzi, tikhoza kujambula 8 – 3 = 5 (diagonal).

Pali 8 vertices kotero jambulani 8 × 5 = 40 (diagonal)

Koma diagonal iliyonse imawerengedwa kawiri, kotero nambala yojambulidwa ndi: 40: 2 = 20 (diagonal).

Fomula yanthawi zonse ya fomu iyi ikhoza kujambulidwa motere 𝒏 × (𝒏 − ): ndi 𝒏 ndi nambala yachilengedwe ndi >.

Phunziro 2: Lolani ABCD quadrilateral monga momwe zasonyezedwera. Jambulani mizere iwiri kuti mupeze 6 quadrilaterals.

Yankho

Itha kujambulidwa monga momwe zilili pansipa. Ndiye 6 quadrilaterals ndi: AEGD; AHKD; ABCD; EHKG; EBCG; Mtengo wa HBCK.

phunziro 3: Tiyeni tibzale mitengo 11 m’mizere 10 ya mitengo itatu iliyonse?

Yankho

Angabzalidwe molingana ndi chithunzi chomwe chili pansipa.

Phunziro 4: Lumikizani pakati pa mbali ya bwalo loyamba kuti mupeze lalikulu lachiwiri. Lumikizani pakati pakati pa mbali ya bwalo lachiwiri kuti mupeze lalikulu lachitatu, ndi zina zotero….

Pezani chiwerengero cha makona atatu pachithunzi chotere mpaka 100th square?

Yankho

Malinga ndi mutuwu, tili ndi tebulo lotsatirali

Chiwerengero cha makona atatu opangidwa ndi: 4 × 99 = 396 (makona atatu).

Fomula yodziwika bwino ya fomu iyi ikhoza kujambulidwa motere 𝟒 × (𝒏 − 𝟏) 𝒗 th kujambula.

Fomu 2: Masamu okhudza kudula jigsaw

Kudula chithunzi choperekedwa m’mawonekedwe ang’onoang’ono ambiri ndikuchiphatikiza mu mawonekedwe ena molingana ndi zofunikira za vuto la masamu ndizovuta kwambiri, zomwe zimafuna kuti ophunzira azitha kusinthasintha, kumbukirani kuyang’anitsitsa mawonekedwe ndi kukula kwa chiwerengero choperekedwa ndi chithunzi. kuti asonkhanitsidwe, chiwerengero cha zidutswa zoti zidulidwe. Kuchokera pamenepo neneratu zomwe zingatheke. Yesani ndikusankha kupeza yankho lolondola.

Zochita zowonetsera

Phunziro 1: Ganizirani pepala lamakona anayi m’litali ndi 4cm mulifupi. Dulani chidutswa chilichonse monga momwe chikuwonetsedwera ndikuchibwezeretsanso kukhala lalikulu?

Yankho

Dulani ndi kufanana monga momwe zilili pansipa:

Phunziro 2: Dulani pepala monga momwe tawonetsera m’munsimu mu zidutswa zinayi kuti mupange lalikulu?

Yankho:

Dulani ndi kufanana monga momwe zilili pansipa:

Phunziro 3: Pansipa pali 14 lalikulu lalikulu. Kodi ndizotheka kudula makadi 7 ang’onoang’ono amakona anayi, iliyonse yomwe ili ndi mabwalo awiri?

Yankho:

Lembani mabwalo 6 monga momwe zilili pansipa. Kuchokera pamenepo, zitha kuwoneka kuti pakona iliyonse yokhala ndi mabwalo awiri odulidwa, pali bokosi loyera limodzi ndi masikweya amtundu umodzi. Chifukwa chake, ngati khadi lomwe lapatsidwa lidulidwa kukhala makadi ang’onoang’ono 7, omwe ali ndi mabwalo 2, padzakhala mabwalo 7 oyera ndi 7 amitundu. Izi sizingachitike chifukwa pali maselo 6 okha amitundu.

Fomu 3: Masamu pa jigsaw puzzles (kuwerengera)

Uwu ndi mtundu wamba wa masamu, ndipo chofunikira kwambiri, ndikufuna kupeza zotsatira zabwino pamayeso

Mu masamu amtunduwu, muyenera kuloweza mafomu owerengera kuzungulira ndi dera. Gwiritsani ntchito mafomuwa mosinthika pavutoli, dziwani kufotokoza mwachidule zomwe zilimo ndikugwiritsa ntchito mwaluso njira zothetsera mavuto kusukulu ya pulayimale, monga kugwiritsa ntchito zithunzi za mizere, kuchepetsa mpaka mayunitsi, kukhazikitsa ma ratio, kugawa magawo, ndi zina zambiri kuti mugwiritse ntchito pa vuto lililonse yankho lolondola, yankho labwino.

Zochita zowonetsera

Phunziro 1: Munda wamakona anayi wozungulira wa 128m. Kuwerengera gawo la dimbalo podziwa kuti m’lifupi mwake ndi 8m lalifupi kuposa kutalika kwake?

Tili ndi chithunzi chotsatira:

Theka lozungulira munda ndi:

128 : 2 = 64 (𝑚)

M’lifupi mwa munda ndi: (64 – 8): 2 = 28 (𝑚)

Kutalika kwa dimba ndi: 28 + 8 = 36 (𝑚)

Dera la munda ndi:

28 × 36 = 1008 (m²).

Yankho: 1008 m²

3. Zochita zolimbitsa thupi

Phunziro 1: Kupatsidwa mfundo 7, zomwe palibe 3 mfundo ndi collinear. Ndi magawo angati a mzere omwe alipo palimodzi pamene mfundo zonse zoperekedwazo zilumikizidwa?
Phunziro 2: Pali mitengo 9, ndiye bzalani mizere 10 ya mitengo itatu pamzere uliwonse?
Phunziro 3: Pezani njira yobzala mitengo 11 m’mizere 10, mitengo itatu pamzere uliwonse?
Phunziro 4: Gwiritsani ntchito machesi 24 kuti mupange mabwalo atatu. Onetsani njira zitatu zokonzera?
Phunziro 5: Dulani pepala la 4 x 9 lamakona anayi mu zidutswa zitatu kuti muphatikize mbali zonse ziwiri?
Phunziro 6: Dulani pepala monga momwe zilili m’munsimu mu zidutswa zisanu kuti muphatikize mbali imodzi?
Phunziro 7: Chithunzi chomwe chili pansipa ndi katoni yokhala ndi mabwalo atatu. Tiyeni tidule katoni kameneka mzidutswa 2 kuti tikaphatikiza pamodzi timapeza masikweya ndipo pakati pakhale dzenje lomwenso ndi lalikulu?
Phunziro 8: Munda wamakona anayi wozungulira wofanana ndi wozungulira wagawo lalikulu la mbali 80m. Werengetsani dera la dimbalo podziwa kuti ngati kutalika kwa mundawo kumachepetsedwa ndi 30m ndipo m’lifupi mwawonjezedwa ndi 10m, dimbalo lidzakhala lalikulu?
Phunziro 9: Munda wamakona anayi wozungulira wa 192m. Ngati kutalika kwake kwachepetsedwa ndi 6m ndipo m’lifupi mwake kuchepetsedwa ndi 4m, mundawu umakhala wofanana. Kuwerengera gawo loyambira?
Phunziro 10: Malo oyanikapo a Xuan Binh Cooperative ndi amakona anayi ndipo m’lifupi mwake ndi ofanana ndi 1 dimension 3.
yaitali. Pokonzekera nyengo yatsopano yokolola, anthu akulitsa bwalo lowumirako mpaka kumagawo atatu (utali wa bwalo), kumanja ndi kumanzere ndi 3m mbali iliyonse. Chifukwa chake, bwalo lidzakhala lalikulu 108m2. Kodi bwalo latsopanoli ndi lalikulu bwanji?
Phunziro 11: Munda wamakona anayi wozungulira 8 m’lifupi mwake. Ngati m’lifupi mwawonjezeke ndi 2m ndipo kutalika kwake kuchepetsedwa ndi 2m, gawo la dimba lidzawonjezeka ndi 144m2. Werengetsani dera la dimba la sukulu mukamakula.
Phunziro 12: dziwe lalikulu, pakati pa dziwe ndi lalikulu chilumba. Madzi otsalawo ndi 1260m2 m’lifupi. Kuzungulira konse kwa dziwe ndi chilumbachi ndi 168m. Kuwerengera m’mphepete mwa dziwe ndi m’mphepete mwa chilumbachi?
Phunziro 13: Rectangle ndi 4cm kutalika ndi 3cm mulifupi. Gawani kutalika mu magawo 4 ofanana, m’lifupi mu magawo atatu ofanana ndikugwirizanitsa mfundozo kuti mupeze mabwalo ang’onoang’ono 12. Kuwerengera kuchuluka kwa zozungulira ndi kuchuluka kwa madera a mabwalo opangidwa mu chithunzi.
Phunziro 14: Minda iwiri yamakona anayi imakhala yozungulira 420m, ngati kutalika kwa munda woyamba kuchepetsedwa ndi 5m ndipo m’lifupi mwake ukuwonjezeka ndi 2m, kuzungulira kwa minda iwiriyi ndi yofanana. Pezani malo ozungulira gawo lililonse?
Phunziro 15: Dera la square ndi 100cm2 lalikulu kuposa dera la rectangle. Mbali ya sikweya ndi 7cm kuposa m’lifupi mwa rectangle ndi 4cm kuchepera kutalika kwake. Kuwerengera mbali ya lalikulu?