Vertically Opposite Angles of Intersecting Lines are Equal

① This example demonstrates that when two lines intersect, the vertically opposite angles are equal. ② The core mathematical concepts involve intersecting lines, vertical angles, angle equality, linear pair properties, and Euclidean geometry fundamentals. ③ The GeoGebra construction uses points A, B, etc., draws segments with the Segment command, creates intersecting lines via Rotate, and measures angles α, β, γ, δ, ε, β_1 with the Angle command to visually confirm the equality of vertical angles. ④ It is designed for middle school geometry, high school Euclidean geometry courses, and teacher demonstrations or inquiry-based learning activities.