Planes in Space and Their Basic Properties

This example demonstrates the fundamental concepts and representations of planes in three-dimensional space. Using objects α and β to denote different planes, along with objects h and a to illustrate points, lines, or relative positions within and between planes, it visually presents the basic properties of planes in solid geometry. It is suitable for assisting high school solid geometry teaching, helping students build spatial awareness and understand the geometric characteristics of planes. The interactive applet allows users to manipulate the configuration of planes and lines, observing how points and lines relate to each other in space. Students can explore key properties such as: three non-collinear points determine a unique plane; if two points of a line lie in a plane, then the entire line lies in that plane; and if two planes share a common point, they intersect along a line passing through that point. Through dynamic visualization, learners can toggle visibility of elements, drag points to see how relationships change, and deepen their understanding of abstract spatial reasoning. This makes it an effective teaching tool for introducing axiomatic foundations of solid geometry and for developing students' ability to think and reason in three dimensions.