Can Special Triangle Lines Be Identical?

This example explores the 'special' lines of a triangle: median, angle bisector, altitude, and perpendicular bisector. It investigates when, if at all, these lines coincide or have unique properties. The construction involves creating a triangle using Polygon, drawing orthogonal lines with OrthogonalLine, finding midpoints with Midpoint, and constructing various bisectors and lines using AngularBisector and LineBisector. The example is suitable for middle school and high school students learning geometric constructions and properties, and can be used for math competition preparation. Key concepts include median theorem, angle bisector properties, altitude and perpendicular bisector definitions, and the relationships between these lines.