HO = RO + EO and ER = EO + RO

Substitution

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

Substitution

Parallel lines form equal corresponding angles

HO = ER

Given

Triangle THO = Triangle MER

HO = HE + EO and ER = EO + RO

ASA (Angle-Side-Angle)

<TOH = <MRE

Segment addition theorem