Parallel lines form equal corresponding angles

Substitution

HO = ER

Substitution

HO = RO + EO and ER = EO + RO

HO = HE + EO and ER = EO + RO

Triangle THO = Triangle MER

Given

RO = HE, <THO = <MER, TO || MR

ASA (Angle-Side-Angle)

<TOH = <MRE

Segment addition theorem