Triangle Inequalities: Exploring Side-Angle Relationships in Triangles

This GeoGebra applet demonstrates the relationship between the largest and smallest angles and their opposite sides in a triangle, allowing users to discover triangle inequalities through interactive manipulation. The core mathematical concepts covered include the triangle inequality theorem, angle-side correspondence, interior angle sum, and classification of acute, right, and obtuse triangles. The construction uses GeoGebra commands Polygon to create triangle poly1, Angle to generate interior angles α, β, γ, Distance to measure side lengths a, b, c and segment d, and text object text1 to display findings. Suitable for middle school geometry instruction and high school preparatory review before trigonometry, this resource supports classroom demonstration and student-led exploration of geometric relationships.