56-Two reflection theorem

Problem 1: Let ABC be a triangle, let A’,B’,C’ such that AA’, BB’,CC’ are parallel and midpoint of AA’,BB’,CC’ lie on a line (d). Let P lie on (d), Denote three lines PA’,PB’,PC’ meet three side lines BC, CA, AB respectively at A1,B1,C1. Show that A1,B1,C1 are colliner.

Problem 2: Let A’B’C’ are reflection of a triangle ABC in line (d). Let P lie on (d). Let three line (d_a),(d_b),(d_c) through P and perpendicular with PA,PB,PC respectively, wich lines meet three side lines B’C’, C’A’, A’B’ respectively at A1,B1,C1. Show that A1,B1,C1 are colliner.