Explore Vertical Angles: Rotation and Angle Measurement

① This GeoGebra example demonstrates the property of vertical angles being equal when two lines intersect, using rotation and triangle construction. ② The core mathematical concept is vertical angles: the pairs of opposite angles formed by intersecting lines are congruent, along with angle measurement, rotational symmetry, and triangle angle relationships. ③ Construction highlights: the Rotate command transforms point A to A', the Angle command creates angles α, β₁, β₂, β₄, γ, and the Segment command builds segments f, g, h, i, forming multiple triangles and angles to dynamically show that vertical angles remain equal under rotation. ④ Suitable for middle school geometry lessons or high school review, this interactive tool helps students intuitively grasp the vertical angle theorem and supports inquiry-based learning.