Geometric Centroid Construction with Isosceles Triangle and Parallelogram

This GeoGebra example demonstrates how to construct the centroid (center of gravity) of geometric figures.①What it shows: Locating the centroid of an isosceles triangle and a parallelogram through intersection of medians, illustrating the 2:1 ratio property where the centroid divides each median.②Math concepts: Geometric centroid/center of mass, triangle medians, parallelogram diagonals, isosceles triangle properties, vector decomposition.③Construction: Use Polygon command to draw triangle ABC and parallelogram ABCD; Midpoint command to find edge midpoints; Segment command to connect vertices with opposite edge midpoints (medians); Intersect command to find centroid G as median intersection; Verify distance ratio between vertex and centroid to midpoint equals 2:1.④Target audience: Middle school geometry (Grade 8), high school vector and coordinate geometry, useful for demonstrating center of mass in physics.