Construction of a 45° Angle with Verification

① This example demonstrates how to precisely construct a 45° angle using GeoGebra's rotation, ray, line, and point tools, with step-by-step logical verification of the construction. ② Core mathematical concepts include the definition of angles, rotational symmetry, basic geometric construction axioms (using rays and lines to define the sides of an angle), and using logical conditions (e.g., whether the target angle reaches 45°) to guide the construction process. ③ Construction highlights: from the summary, the Rotate command is used to rotate points or rays to generate the 45° angle, Angle measures the angle, Ray and Line draw the sides, and Point defines key points; objects include R, S, mAngle, R', α, A, B, B', β, target1, B'_1, γ, target2, step1, step2, finished, g, text1, showAnswer, f, C, h, target3, target4, step3, step4, which work together for stepwise construction and feedback. ④ Suitable for middle school geometry lessons or math lab activities, helping students understand angle construction, rotation operations, and logical verification, and serving as an interactive GeoGebra teaching case.