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```#include <iostream>
using namespace std;

class Segment {
public:
// Constructors
Segment(double x1, double y1, double x2, double y2) {
setEndpoints(x1, y1, x2, y2);
}

Segment(pair<double, double> point1, pair<double, double> point2) {
setEndpoints(point1.first, point1.second, point2.first, point2.second);
}

// Function to check if a segment lies in one quarter of the plane
bool isCompletelyInOneQuarter() const {
return (bothEndpointsInSameQuarter());
}

// Overload the equality operator for segments
bool operator==(const Segment& other) const {
return (this->p1 == other.p1 && this->p2 == other.p2) || (this->p1 == other.p2 && this->p2 == other.p1);
}

private:
std::pair<double, double> p1, p2;

// Helper function to set segment endpoints
void setEndpoints(double x1, double y1, double x2, double y2) {
p1 = make_pair(x1, y1);
p2 = make_pair(x2, y2);
}

// Helper function to check if both endpoints are in the same quarter
bool bothEndpointsInSameQuarter() const {
return (sameQuarter(p1) && sameQuarter(p2));
}

// Helper function to check if a point is in the same quarter of the plane
bool sameQuarter(pair<double, double> point) const {
return (point.first >= 0 && point.second >= 0) || (point.first <= 0 && point.second <= 0);
}
};

// Test function
int main() {
// Create segments
Segment segment1(1.0, 2.0, 3.0, 4.0);
Segment segment2(-1.0, -2.0, 2.0, 2.0);
Segment segment3(2.0, 3.0, 5.0, -1.0);

// Test if segments lie in one quarter
if (segment1.isCompletelyInOneQuarter()) {
cout << "Segment 1 is in one quarter of the plane." << endl;
} else {
cout << "Segment 1 is not in one quarter of the plane." << endl;
}

if (segment2.isCompletelyInOneQuarter()) {
cout << "Segment 2 is in one quarter of the plane." << endl;
} else {
cout << "Segment 2 is not in one quarter of the plane." << endl;
}

if (segment3.isCompletelyInOneQuarter()) {
cout << "Segment 3 is in one quarter of the plane." << endl;
} else {
cout << "Segment 3 is not in one quarter of the plane." << endl;
}

// Test equality of segments
if (segment1 == segment2) {
cout << "Segment 1 is equal to Segment 2." << endl;
} else {
cout << "Segment 1 is not equal to Segment 2." << endl;
}

if (segment1 == segment3) {
cout << "Segment 1 is equal to Segment 3." << endl;
} else {
cout << "Segment 1 is not equal to Segment 3." << endl;
}

return 0;
}
```  