Given: RO = HE, ∠THO = ∠MER, TO ǁ MR

Prove: △THO ≅ △MER

Parallel lines form equal corresponding angles
Substitution
HO = ER
RO = HE, ∠THO = ∠MER, TO ǁ MR
Substitution
HO = RO + EO and ER = EO + RO
HO = HE + EO and ER = EO + RO
△THO = △MER
Given
ASA (Angle-Side-Angle)
∠TOH = ∠MRE
Segment addition theorem