Geometry began as practical mensuration (this means, they assumed any
two numbers could be expressed in terms of another - they didn't realize
irrational numbers existed). In 2000 to 1600 B. C. there is evidence that
the Babylonians had general rules for the area of a rectange, the areas
of right and isosceles triangles (maybe even a general triangle), the area
of a trapezoid having one side perpendicular to the parallel sides, the
volume of a rectangular parallelepiped, and the volume of a right prism
with a special trapezoidal base. They did not understand pi at this time,
but took the circumferenc of a circle to be three times the diameter and
the area as one-twelfth the square of the circumference (which equates to
pi being three).
All this geometry was intuitive. There was no demonstrating or deductive
reasoning. This was the time of the Ahmes Papyrus, which listed the area
of isosceles triangles as 1/2 b*h, and the area of a circle as (d - 1/9d)^2,
where d = diameter.
Indians had the same amount of mensurations, as did the Romans. They were
interested in geometry only for its practical value. This included measurement
of land, laying out of cities, engineering, warfare.