Constructing Supplementary Angles with Angle Bisectors

This example demonstrates how to construct and verify supplementary angle relationships in a dynamic geometry setting: two rays form angles whose measures sum to 180°, and the construction computes and displays the relevant angles and their status. The main mathematical concepts are supplementary angles, angle measurement, conditional logic, and the role of angle bisectors in geometric construction. Construction highlights in GeoGebra include using Intersect and Point to define the vertex and key intersection points (e.g., objects like A, B, C and angle labels such as α, β, γ, δ), Vector to represent ray directions (u, v, w), Rotate to generate rotated ray configurations, and Angle to measure and display angle values. Textfield and text objects are used to annotate angles, AngularBisector is applied to construct bisectors, and If provides conditional display/verification of the supplementary condition. InputBox and button controls (button1, button2) support switching scenarios or inputs. Suitable for middle/high school geometry lessons, dynamic geometry practice, and interactive classroom demonstrations.