Final answer:
Plane geometry is the branch of mathematics that focuses on the study of two-dimensional objects, such as squares and tiles, commonly in the context of Euclidean space.
Step-by-step explanation:
The subject that deals with two-dimensional objects such as squares and tiles is plane geometry. Plane geometry is a branch of mathematics that focuses on the properties and relations of points, lines, surfaces, and shapes on a flat plane. Euclidean geometry, which is a system based on the work of the ancient Greek mathematician Euclid, is a common example where we investigate these relationships in a 'flat' space. In this flat space, Euclidean geometry dictates that a straight line is the shortest path between two points, the angles in any triangle add up to 180 degrees, and parallel lines never intersect. Such properties are fundamental in comprehending two-dimensional kinematics and geometric transformations.