This study investigates the impact of active listening and mirroring behaviors on intimacy and trust in human-robot interaction. Based on the principles of effective human communication, active listening and mirroring were adapted for robotic systems to enhance relationship dynamics like intimacy, negative attitudes, and trust. The experimental setup involved a social robot to exhibit non-verbal cues that aligned with active listening and mirroring during interactions in the cooking scenario. The participants experienced two conditions: active listening and active listening with mirroring. The results indicated that the combination of active listening with mirroring significantly enhances intimacy and perceived trust compared to active listening only, while there is no significant difference in reducing negative attitudes. These findings suggest that incorporating non-verbal cues can substantially improve engagement in human-robot interactions, making robots more relatable and trustworthy companions.