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

Prove: Triangle THO = Triangle MER

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