Final answer:
To demonstrate that a normal line to a point on the Earth's surface is perpendicular to that point, it is effective to draw a tangent at that point. The tangent will be perpendicular to the radius of the Earth at the point of contact, illustrating a fundamental geometric principle.
Step-by-step explanation:
To illustrate to an elementary class of students that a normal line to a point on the Earth's surface is perpendicular to that point, it's a good idea to draw a tangent at that point. A tangent in geometry is a line that touches a curve at a single point without crossing it. In the case of the Earth, which can be modeled as a sphere, a tangent line at any point on the surface would be perpendicular to the radius of the Earth at that point—a concept that can be further clarified using the figure-ground relationship to separate the surface (like a 2D ground on a sheet of paper) and the line (as a figure emerging from that surface).
By understanding that a tangent only touches the sphere at a single point and is perpendicular to the radius, students can learn about fundamental geometric principles that also apply to more complex shapes like the Earth. This concept can be demonstrated by drawing a line from the point on the Earth's surface, through the center of the earth, forming a radius (OB), and then drawing the tangent line at that point on the surface, ensuring it makes a 90° angle with the radius. This relationship is based on Pythagorean theorem and the core concepts of geometry, and it helps students visualize how lines and angles work in three dimensions.