Let ABC be a triangle. Let C′ and A′ be the reflections of its vertices C and A, respectively, in the altitude of triangle ABC issuing from B. The perpendicular to the line BA′ through the point C′ intersects the line BC at U; the perpendicular to the line BC′ through the point A′ intersects the line BA at V. Prove that UV∥CA.
Darij geometrygeometric transformationreflectiongeometry proposed