Given a triangle ABC, let A′,B′,C′ be the perpendicular feet dropped from the centroid G of the triangle ABC onto the sides BC,CA,AB respectively. Reflect A′,B′,C′ through G to A′′,B′′,C′′ respectively. Prove that the lines AA′′,BB′′,CC′′ are concurrent. geometrygeometric transformationreflectionparallelogramhomothetyratiogeometry proposed