Relative Positions of Two Lines in the Plane - Lesson+Exploration+Practice

① This example demonstrates the three relative positions of two lines in a plane—intersecting, parallel, and coincident—through an interactive dynamic geometry environment with exploration and practice components. ② Core mathematical concepts include slope, intercept, intersection point, conditions for parallelism and perpendicularity, and how parameter changes affect line relationships. ③ Construction highlights: uses GeoGebra commands such as Line to create lines, Intersect to find intersection points, Vector and Translate for translation vectors, Polygon and PointIn for auxiliary shapes, SelectedIndex with a dropdown menu (ddMenu) to switch between cases, a slider (speed) to control animation, and warning objects (warningOutside, warningParallel) to flag special situations. ④ Suitable for middle or high school geometry/analytic geometry classes, serving as an introduction, exploratory activity, or practice tool to help students grasp the criteria for determining relative positions of two lines.