Given: RO = HE, ∠THO = ∠MER, TO ǁ MR

Prove: △THO ≅ △MER

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