From the Wikipedia link for Geometry:
Geometry (Ancient Greek: γεωμετρία; geo- "earth", -metron "measurement") is a branch of mathematics concerned with questions of shape, size, relative position of figures, and the properties of space.
Up to the work of Riemann and Gauss, this definition would have made clear to me examples of geometrical objects: a line, square, cube, hypercube; each of these possessing geometrical properties such as the number of sides, angles between faces, the dimension of space that contains them etc. Hence a geometrical object was a set of measurements associated with an object using a ruler.
After the work of Einstein and Minkowski who showed that time and space were a part of one another, would it be correct to say:
a geometrical object is a set of measurements associated with an object of distance and time using a ruler and a clock ?
Geometrical objects includes an interval of time, the invariant space-time interval?