Constructing and Measuring the Angle Between Two Planes

This example demonstrates how to construct and measure the angle between two planes in 3D space. The key ideas include the definition of the angle between planes, geometric relationships involving plane intersection, and the use of direction information such as normal vectors (or equivalent vectors) to determine the correct angle. In GeoGebra, the construction leverages IntersectPath and LeftSide to build the relevant configuration around the intersection region, Point and PointIn to place points at structurally meaningful locations, Vector to represent directions, and Segment to form geometric entities used to visualize the angle. Finally, Angle is used to compute the angle, with plane objects (Π_1, Π_2), auxiliary objects (points/vectors like a, b, u, v), and labeled angle measures (θ, β, γ, α, δ, etc.) to present the result clearly. Suitable for upper secondary students and introductory geometry/vector courses, as well as teaching demonstrations and exploratory modeling with GeoGebra.