Parallel lines form equal corresponding angles

Substitution

HO = ER

RO = HE, ∠THO = ∠MER, TO ǁ MR

Substitution

HO = RO + EO and ER = EO + RO

HO = HE + EO and ER = EO + RO

△THO = △MER

Given

ASA (Angle-Side-Angle)

∠TOH = ∠MRE

Segment addition theorem