Medians and Perpendicular Bisectors of a Triangle

This GeoGebra activity demonstrates the construction of the three medians (segments from each vertex to the midpoint of the opposite side) and the three perpendicular bisectors (lines through each side's midpoint perpendicular to that side) of a triangle, allowing students to observe the intersection points of each set. Core mathematical concepts include triangle medians, centroid, perpendicular bisectors, circumcenter, and the relationships between midpoints and perpendicularity. Construction details: using the Segment command to draw the triangle sides, the Midpoint command to locate side midpoints, then constructing medians by connecting vertices to midpoints, and perpendicular bisectors by drawing lines through midpoints perpendicular to the sides. Key objects include vertices A, B, C, sides f, g, h, midpoints D, E, F, and the derived medians f_1, g_1, h_1 and perpendicular bisectors D_1, E_1, F_1, with text labels. Suitable for middle school geometry lessons to explore the properties of triangle centers (centroid and circumcenter) and geometric construction techniques.