Construct Perpendicular Lines (Example #13)

This GeoGebra example demonstrates how to construct a line perpendicular to a given line through a specified point using basic geometric construction tools. The core mathematical concept is the definition of perpendicularity and the classical compass-and-straightedge method, which relies on equal distances from a circle to determine the right angle. The construction uses the Circle command to draw a circle centered at the given point, intersecting the original line at two points; then, using these intersection points as centers, equal-radius circles are drawn, and the line connecting their intersection points is the perpendicular. Finally, Point and Segment commands are used to mark key points and draw the perpendicular segment. This example is suitable for middle school geometry lessons, helping students understand the logic behind perpendicular construction while familiarizing them with essential GeoGebra commands.