Final answer:
Iago manipulates Roderigo into believing Desdemona and Cassio are lovers by planting a handkerchief and using his perceived honesty as implicit proof. Roderigo is blinded by his infatuation with Desdemona and thus is susceptible to Iago's lies.
Step-by-step explanation:
In Shakespeare's Othello, Iago uses various forms of manipulation and deceit to convince Roderigo that Desdemona and Cassio are involved in an affair. Iago's so-called "proof" includes planting Desdemona's handkerchief on Cassio, which is later used to falsely demonstrate that Cassio has been intimate with Desdemona. Roderigo's inability to see through Iago's lies is primarily due to his own infatuation with Desdemona, which blinds him to reality and leads him to trust Iago's malicious fabrications.
Moreover, Iago is seen as an honest man by those around him; this perceived honesty serves as an unstated proof of his claims about Desdemona and Cassio. Roderigo's desperation to win Desdemona's affection makes him an easy prey for Iago, as he clings to any hope provided by Iago, even if it rests on unfounded accusations and manipulations.