Exploring Parallel and Perpendicular Lines (Copy)

This interactive GeoGebra example dynamically demonstrates the properties and criteria of parallel and perpendicular lines. It visually explores the relationships between slopes, the geometric conditions for parallelism and perpendicularity, and verifies related theorems through construction. Key construction steps: use the OrthogonalLine command to create perpendicular lines, Point, Intersect, Segment, Line, Vector, and Translate commands to build the basic figures and perform translations to generate parallel lines. Objects include lines c, m, a, b, e, d, j, h, g, f, k, i, l; points A, B, C, D, E, F; translated points B', C', D'; and text labels text1, text2, text3. Suitable for middle and high school students learning plane geometry, ideal for classroom demonstrations or self-study to understand the theorems of parallel and perpendicular lines and their coordinate representations.