If AB = AD, then you have that triangle ABD is an isosceles triangle (it has two equal sides). If it is isosceles, then the angles opposite to angles those equal sides must be equal. Then angle ADB = . and by the property of all internal angles of a triangle have to add to , we get that:
The equations have the same slope but different y-intercepts. This means the lines are parallel and there is no solution (since they do not intersect).
