Why do we learn math in school? To learn how to manipulate abstract objects according to a set of abstract rules.
Geometry is the most useful mathematical subject because the way problems are solved is closest to real life. Read the paragraph imagining that you can apply the same principles to planning a trip or applying to a college.
You have a set of tools and simply need to choose which one to use. There are often more than two ways to reach the answer, depending on the set of tools you choose.
The tools used to solve the problem may belong to entirely different realms: vectors, linear systems, or circumscribed circles.
You can start from almost any point and still arrive at the answer, sometimes not in the most efficient way. Or you may never get there and realize that you need to start from a different point.
You can easily outperform your mentor in solving the problem efficiently once you learn some tricks. And you can invent new ones by combining the old ones.
And finally, there is room for tragedy in geometry.
Students were given a simple problem: in a right triangle, the hypotenuse is 10 and the height to it is 6. What is the area of the triangle?
Regular students gave the quick answer, while the smart students could not.