Vertically Opposite Angles: Equal Angles from Intersecting Lines

①This example demonstrates the property of vertically opposite angles: when two lines intersect, the angles opposite each other are equal.②The core mathematical concept is the vertically opposite angles theorem, which states that intersecting lines create pairs of equal opposite angles, while adjacent angles are supplementary.③Construction: Using GeoGebra commands, two segments (Segment) are drawn to form intersecting lines, the intersection point E is found with the Intersect command, and four angles α, β, γ, δ are measured with the Angle command. A text object (text1) displays the angle values, allowing users to verify equality dynamically.④This is suitable for middle school geometry lessons or self-study, helping students grasp angle relationships in intersecting lines, and can be used as an interactive demonstration where dragging the lines updates the angles while the opposite pairs remain equal.