look/cpp/task2/task1.3.cpp

#include <iostream>
#include <cmath>

using namespace std;

const double EPS = 1e-9;

string xuo3(double x1, double y1, double x2, double y2, double x3, double y3, double x4, double y4) {
    auto dist = [](double x1, double y1, double x2, double y2) {
        return sqrt((x2 - x1) * (x2 - x1) + (y2 - y1) * (y2 - y1));
    };

    auto isParallel = [](double x1, double y1, double x2, double y2, double x3, double y3, double x4, double y4) {
        return abs((y2 - y1) * (x4 - x3) - (x2 - x1) * (y4 - y3)) < EPS;
    };

    auto isPerpendicular = [](double x1, double y1, double x2, double y2, double x3, double y3, double x4, double y4) {
        return abs((x2 - x1) * (x4 - x3) + (y2 - y1) * (y4 - y3)) < EPS;
    };

    bool ab_parallel_cd = isParallel(x1, y1, x2, y2, x4, y4, x3, y3);
    bool bc_parallel_da = isParallel(x2, y2, x3, y3, x1, y1, x4, y4);
    bool ab_perpendicular_bc = isPerpendicular(x1, y1, x2, y2, x2, y2, x3, y3);
    bool bc_perpendicular_cd = isPerpendicular(x2, y2, x3, y3, x3, y3, x4, y4);

    if (ab_parallel_cd && bc_parallel_da) {
        if (ab_perpendicular_bc && bc_perpendicular_cd) {
            return "Прямоугольник";
        }
        return "Параллелограмм";
    }

    if (ab_parallel_cd || bc_parallel_da) {
        return "Трапеция";
    }

    return "Произвольный четырехугольник";
}

int main() {
    double x1, y1, x2, y2, x3, y3, x4, y4;
    cout << "Введите координаты точек A, B, C, D (x1 y1 x2 y2 x3 y3 x4 y4): ";
    cin >> x1 >> y1 >> x2 >> y2 >> x3 >> y3 >> x4 >> y4;

    string type = xuo3(x1, y1, x2, y2, x3, y3, x4, y4);
    cout << "Тип четырехугольника: " << type << endl;

    return 0;
}