Answer:
For all the proofs you start with the given, and work you’re way down the problem.
1)
Statement Reasoning
LM=NO Given
∠LMO≅∠NOM. Given
OM=OM Reflexive Property of Equality
ΔLMO=ΔNOM SAS Congruence Postulate
2)
Statement Reasoning
∠A=∠D Given
CB bisects ∠ACD Given
CB=CB Reflexive Property of Equality
∠ACB=∠BCD Definition of Angle Bisector
∠ABC=∠CBD Definition of Angle Bisector
ΔABC=ΔDBC ASA Congruence Postulate
CA=CD Definition of Congruence
3)
Statement Reasoning
∠T=∠U Given
S is midpoint of TU Given
∠TSN=∠USH Vertical angles are congruent
TS=SU Definition of Midpoint
ΔTSN=ΔUSH ASA Congruence Postulate
SN=SH Definition of Congruent