Geometric Construction for Counterclockwise Rotation

This example demonstrates how to perform a counterclockwise rotation in the plane and visualize the resulting correspondence between the original and rotated points/segments, emphasizing the preserved angle and distance relationships. The key mathematical ideas include rotation as a rigid transformation, angle measurement for a specified counterclockwise direction, and interpreting properties that follow from the rotation’s invariance (e.g., consistent midpoint/related segment behavior when used in constructions). Construction highlights from the provided GeoGebra summary: it uses Segment to create the starting segment(s), Rotate to generate rotated objects (such as B to B'), Angle to define or display the rotation angles (α and β), and Distance to measure relevant lengths before and after rotation. The involved objects include points like C and B, the rotated image points (B′), and angle/measurement placeholders (pic1/pic1′, g, β, a). Suitable for middle/high-school geometry, transformation chapters, and anyone learning to understand “rotation → angle → distance invariance” through interactive construction.