HO = RO + EO and ER = EO + RO

Parallel lines form equal corresponding angles

△THO = △MER

HO = HE + EO and ER = EO + RO

Given

RO = HE, ∠THO = ∠MER, TO ǁ MR

ASA (Angle-Side-Angle)

HO = ER

Substitution

Substitution

∠TOH = ∠MRE

Segment addition theorem