Final answer:
The statement is true: in Euclidean geometry, a point has no dimensions, a line has one dimension (length), and a plane has two dimensions (length and width). These form the foundational elements of Euclidean geometry, describing the space in which we represent points, lines, and planes.
Step-by-step explanation:
The statement presented is true: in Euclidean geometry, a point has no length, width, or height, a line has infinite length but no width or height, and a plane has infinite length and width but no height. To understand these concepts, consider the following definitions:
- A point is an exact position or location on a plane surface. It is represented by a dot and has no dimension.
- A line is an endless collection of points extending in two opposite directions. It has one dimension, length.
- A plane is a flat, two-dimensional surface that extends infinitely far. A plane has two dimensions, length and width.
These are foundational concepts in Euclidean geometry, which is used to describe the space around us in terms of points, lines, planes, and figures. This geometry assumes a flat space and basic principles, such as the shortest distance between two points is a straight line, and the sum of angles in a triangle is 180 degrees.