Open Middle Challenge: How Close to Perpendicular Can You Get?

This is an Open Middle-style geometry challenge that explores how close two straight lines can be to being perpendicular. The core mathematical concepts involve slope of a line, the perpendicular condition (product of slopes equals -1), angle measurement, and linear equations in coordinate geometry. Construction highlights: using GeoGebra commands such as Point, Slope, Intersect, and Angle to create two lines and their intersection, while Textfield and InputBox provide interactive input fields for users to adjust slopes or line equations and observe the angle change in real time. Additional commands like Length and Mode help display distances and modes, and button1 with the correct object enables automatic answer checking. This example is suitable for upper middle school to high school students, reinforcing the criteria for perpendicular lines, fostering number-sense and inquiry-based learning, and serving as an interactive challenge in classroom settings.