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

Prove: Triangle THO = Triangle MER

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