Let ABCD be a square, and let E and F be points in AB and BC respectively such that BE=BF. In the triangle EBC, let N be the foot of the altitude relative to EC. Let G be the intersection between AD and the extension of the previously mentioned altitude. FG and EC intersect at point P, and the lines NF and DC intersect at point T. Prove that the line DP is perpendicular to the line BT. analytic geometrygraphing linesslopegeometrysimilar triangles