Үйге тапсырма беру: R = 25 мм деп алып, біросьті сопақша сал.
Сабақ: №
Сабақтың тақырыбы:
Параллель проекциялау әдісі.
Сабақтың мақсаты:
а) Білімділік: Оқушыларға сызу құралдарын қолдану амал тәсілін
үйрету, жаңа мағлұмат беру және т.б.
ә) Дамытушылық: Сабақ оқытудың негізгі үрдісін есте қалдыру,
оқушы санасына терең сіңіру.
б) Тәрбиелілік: Сызу арқылы оларды тазалыққа, ұқыптылыққа
үйрету.
Сабақтың көрнекілігі: А4 пішіміндегі қағаз, қарындаштар, сызғыш, өшіргіш, шеңберсызар және тағы басқа.
Сабақтың өту барысы:
Ұйымдастыру кезеңі.
Үйге берілген тапсырманы тексеру.
Жаңа тақырыпты түсіндіру.
Тапсырмаларды орындау.
Сабақты бекіту.
Үйге тапсырма.
Сабақтың барысы:
Сызбада нәрсенің кескінін салу керек. Нәрсенің кескінін калай салады? Кескін проекциялау әдісімен салынады. Проекциялау әдісін түсіндірейік. Бізге А нүктесінің π' жазықтығындағы кескінін салу керек болсын (27, а-сурет). Ол үшін π' жазықтығында жатпайтын s түзуін алайық. Егер түзудің екі нүктесі бір жазықтықта жатса, ол түзудің басқа нүктелері де сол жазықтықта жатады, яғни түзу жазықтықта жатады. Түзу жазықтықта жатса, ол түзудің барлық нүктелері де осы жазықтықта жатады. Сонымен, жазықтық пен ол жазықтықта жатпайтын түзудің бірден артық ортақ нүктесі болуы мүмкін емес.
Түзу мен жазықтықтың ортақ нүктесін олардың қиылысу нуктесі дейді. Егер түзу мен жазықтықтың ортақ нүктесі болмаса, оларды параллель деп атайды. Түзу берілген жазықтыққа параллель болуы үшін, ол жазықтықтың бір түзуіне параллель болуы қажет. А нүктесінің π' жазықтығындағы кескіні А' нүктесін былай саламыз: А нүктесі арқылы s түзуіне параллель етіп а түзуін жүргіземіз (27, ә-сурет). Сонда а түзуі π' жазықтығымен А' нүктесінде қиылысады. А' нүктесін А нүктесінің π' жазықтығындағы s бағытындағы параллель проекциясы деп атайды.
π' жазықтығын проекциялар жазықтығы, s түзуін проекциялау бағыты және а түзуін проекциялаушы түзу деп атайды.
Берілген l түзуінің π' жазықтығындағы кескінін тұрғызу үшін, оның екі (А мен В) нүктесін s бағытында π' жазықтығына проекциялаймыз (28, а-сурет). Табылған проекцияларды, яғни А' пен В' нүктелерін қосатын Ғ түзуі берілген I түзуінің параллель проекциясын анықтайды.
ABC үшбұрышының π' жазықтығындағы кескінін тұрғызу үшін, оның төбелерін π' жазықтығына s бағытында проекциялаймыз (28, ә-сурет). А' нүктесі А нүктесінің, В' нүктесі В нүктесінің, С нүктесі С нүктесінің параллель проекциясы. A'B'C үшбұрышы — ABC үшбұрышының параллель проекциясы.
Қисық сызықтың кескінін алу үшін, оның бойынан мүмкіндігінше тығыз орналасқан нүктелер жиынын аламыз. Берілген l сызығының бойынан A, В, С, ... нүктелерін аламыз (28, б-сурет). Олардың π' жазықтығындағы проекциялары A', S', С',... арқылы жүргізілген қисық сызық (l') берілген сызықтың параллель про- екциясы болады. Сонымен, нәрсенің жазықтықтағы кескінін салу үшін, оның нүктелерін сол жазықтыққа проекциялау керек. Нүктенің проекциясын алу үшін берілген нүкте арқылы проекциялаушы түзу жүргіземіз. Проекциялаушы түзудің проекциялар жазықтығымен қиылысу нүктесі берілген нүктенің проекциясын береді. Нәрсе нүктелерінің табылған проекцияларын белгілі тәртіппен қосамыз.
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)
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)
Үйге тапсырма беру: 30, б суретте LМN үшбұрышының проекциясы кескінделген. Үшбұрыш медианаларының проекцияларын сал.
Сабақ: №
Сабақтың тақырыбы:
Тік бұрыштап проекциялау әдісі.
Сабақтың мақсаты:
а) Білімділік: Оқушыларға тік бұрышты проекциялау түрін
таныстыру.
ә) Дамытушылық: Тік бұрышты проекциялаудың әдісін меңгеру
мақсатында сабақты дамыту.
б) Тәрбиелілік: СТО бағдарламасының әдістері арқылы
оқушылардың ой-танымдық қабілеттерін дамытып,
тәрбиелеу.
Сабақтың көрнекілігі: А4 пішіміндегі қағаз, қарындаштар, сызғыш, өшіргіш, шеңберсызар және тағы басқа.
Сабақтың өту барысы:
Ұйымдастыру кезеңі.
Үйге берілген тапсырманы тексеру.
Жаңа тақырыпты түсіндіру.
Тапсырмаларды орындау.
Сабақты бекіту.
Үйге тапсырма.
Сабақтың барысы:
Нәрсенің тікбұрышты проекциясын салуды тік бұрышты проекциялау дейді. Проекциялар жазықтығына перпендикуляр түзулер проекциялаушы түзулер болады. Проекциялаушы түзулер нүктеге проекцияланады.
Нәрсенің параллель проекциясын салу үшін проекциялар жазықтығын және проекциялау бағытын беру керек болса, оның тік бұрышты проекциясын салу үшін проекциялар жазықтығының берілуі жеткілікті. Проекциялар жазықтығына параллель жазық фигура өзінің пішінін және өлшемдерін сақтап, проекцияланады. Жазық фигура деп – барлық нүктелері бір жазықтықта жататын фигураны айтады.
Центр деп аталатын нүктеден бірдей қашықтықтағы жазық нүктелерінің геометриялық орнын шеңбер деп атайды.
Проекциялар жазықтығына параллель жазықтықты деңгейлік жазықтық деп атайды. Деңгейлік жазықтықта жатқан кесінді, жазық фигура бұрмаланбай, өздерінің пішіндерін, өлшемдерін сақтап, проекцияланады. Проекциялар жазықтығына перпендикуляр жазықтықты проекциялаушы жазықтық деп атайды.
Берілген А нүктесінің π' жазықтығындағы кескінін салу үшін одан π' жазықтығына перпендикуляр түсірейік (31, а-су- рет). Жазыктыққа перпендикуляр деп сол жазықтықпен 90' бұрыш жасайтын түзуді айтады. Жазықтыққа перпендикуляр түзу жазықтықтың барлық түзулерімен де 90º-қа тең бұрыш жасайды, яғни оның барлық түзулерше де перпендикуляр болады. Берілген түзу берілген жазықтыққа перпендикуляр бола ма? Оны қалай білуге болады? Түзудің жазықтыққа перпендикулярлық белгісі — түзу жазықтықтың қиылысатын екі түзуіне перпендикуляр болуы қажет. Бұл айтылғанның дұрыстығы стереометрияда дәлелденеді.
А' нүктесінде қиылысатын а және b түзулері π' жазықтығында жатыр делік (31, ә-сурет). Егер А және А' нүктелері арқылы анықталатын түзу а және b түзулерінің әрқайсысына да перпекдикуляр болса, онда АА' түзуінің π' жазықтығына да перпендикуляр болғаны, Сонымен, АА' түзуі — А нүктесінен π'-қа түсірілген перпендикуляр. Перпендикуляр мен жазықтықтың қиылысу нүктесін перпендикулярдың табаны деп атайды.
А нүктесінен π' жазықтығына түсірілген перпендикулярдың табанын, яғни А' нүктесін А нүктесінің π' жазықтығындағы тікбұрышты проекциясы дейді.
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)
Достарыңызбен бөлісу: |