@Zeyad,
two different issues and questions there.
1. it's fine in many cultures for men and women to hang out together, without being in a relationship.
fair enough that she didn't want to upset you
2. it's not fine to lie.
not fair to lie about the hang-outs
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if you'd been cool about her time with your other friend, she might not have felt the need to lie. you both have some work to do here before you get into future relationships.