Ребят, нужна ваша помощь! Задали прорешать десять задач по геометри, я ничего не понимаю. Пыталась сама решать но ответ не сходится. помог

Ребят,очень нужна ваша помощь!Задали прорешать десять задач по геометри,я ничего не понимаю.Пыталась сама решать но ответ не сходится.

Пожалуйста помогите решить!Если можете то подробное решение напишите.

  • Я так- галопом :))) если покажется, что я сразу ответ написал - разбирайтесь, все пункты РЕШЕНЫ (просто "для учителя" надо записать это решение "как надо")

    1.

    Ф1 + Ф2 = 180;

    Ф1/Ф2 = 7/8;

    Пусть Ф1 = 7*х; Ф2 = 8*x; тогда 15*x = 180, x = 12; но х = Ф2 - Ф1.

    2.

    Высота к основанию делит треугольник на два Пифагоровых (8,15,17) (разберитесь! Пифагоров треугольник - это ПРЯМОУГОЛЬНЫЙ ТРЕУГОЛЬНИК с целыми длинами сторон, вроде 3,4,5 или 5,12,13. А почему он - прямоугольный?)

    3.

    Диагонали делят ромб на 4 Пифагоровых треугольника (7,24,25).

    То есть сторона ромба 25, а площадь 14*48/2 = 336

    4.

    Радиус окружности равен высоте правильного треугольника со стороной 12, то есть

    r = 12*√3/2 = 6*√3; S = π*r^2 = 108*π

    5.

    Тут-то что не понятно? 30 - 16 = 14; 30 + 16 = 46; второй класс начальной школы.

    6.

    Если описать вокруг любого правильного многоугольника окружность, то очень просто доказать, что центральный угол, соответствующий стороне, равен внешнему углу при вершине (я вообще-то не обязан это тут писать, но - мало-ли, вдруг "станет понятно" :) докажите это).

    180 - 135 = 45; n = 360/45 = 8;

    7.

    По теореме косинусов (BC = x)

    7^2 = 8^2 + x^2 - 2*x*8*(1/2); x^2 - 8*x + 15 = 0; (x - 3)*(x - 5) = 0;

    8.

    Условие неверное, надо добавить "проведенные из одной точки".

    Диаметр 6*2 = 12, хорда 12*cos(30) = 6*√3

    9. и 11.

    Треугольник со сторонами 13,14,15 "составлен" из двух Пифагоровых (5,12,13) и (9,12,15), так, что катеты 5 и 9 вместе образуют сторону 14. Поэтому высота к стороне 14 равна 12 (в условиях это не спрашивается, ну и ладно), и косинусы углов при стороне 14 равны 5/13 и 9/15 = 3/5

    10.

    Высота делит прямоугольный треугольник на два, ему же подобных (и - между собой, конечно). Поэтому

    h/8 = 18/h; h^2 = 8*18; h = 12;

    c = 8 + 18 = 26;

    S = c*h/2 = 26*12/2 = 156. На вложенном рисунке дан вдвое больший ответ. 

     

     

    Примечание :) 

    При оформлении решений "в тетрадь" надо заменить ссылки на Пифагоровы треугольники "обычными" рассужденими. Например, в пункте 2. следует писать так

    "проведем высоту к основанию, которая делит его пополам, поскольку треугольник равнобедренный. В одном из получившихся прямоугольных треугольников гипотенуза 17, катет 16/2 = 8, поэтому второй катет h^2 = 17^2 - 8^2 = 225; h = 15;"

    Для пунктов 9, 11 этот момент не так-то и прост.

    Надо провести высоту к стороне 14. Далее есть два пути нахождения этой высоты и отрезков, на которые она делит сторону 14.

    а. тупой - по формуле Герона площадь треугольника равна 84, откуда высота 12. Дальше из прямоугольных треугольников находятся отрезки по теореме Пифагора.

    б. немного более умный - сразу надо записать теоремы Пифагора для обеих прямоугольных треугольников, на которые высота делит весь треугольник. Если обозначить их x и y, то

    x^2 + h^2 = 13^2;

    y^2 + h^2 = 15^2;

    x + y = 14;

    Решаете, получаете x = 5; y = 9; h = 12.

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