67-A generalization of Christipher Zeeman's theorem

Let $ABC$ be a triangle, let a line $(d)$ cut the sidelines $BC,CA,AB$ at $A_1,B_1,C_1,$ denote $H_A,H_B,H_C$ are the orthocenter of $AB_1C_1, BC_1A_1$, $CA_1B_1$ ; Denote $A',B',C'$ are reflection of $A$ in midpoint of $B_1C_1$; $B$ in midpoint of $C_1A_1$; C in midpoint of $A_1B_1$ respectively.

Theorem 1: Three line through $H_A,H_B,H_C$ and parallel to $BC,CA,AB$ form a triangle congruent and inversely homothety to $ABC$

Theorem 2: Three line through $A',B',C'$ and parallel to $BC,CA,AB$ form a triangle congruent and homothety to ABC, the homothety at infinity