Let ABC be an isosceles triangle at A. Let D be the midpoint of BC. On segment AD take any point E (E is different from A and D). Through E draw lines perpendicular to AB and AC at M, N, respectively. a) Prove that quadrilateral AMEN is a square.

b) Prove MN // BC.

c) Through M draw a line perpendicular to DN at F. Prove angle AFE = 90 degrees

d) Prove that B, E, F are collinear.