How to approach a random person that appears to be interested in you?

Question

A lot of the time (3-5 times a month) when I'm walking in the street or sitting on the public transit random strangers will make eye contact with me for more than 3 seconds and also smile at me in a way as if they want me to talk to them or something. In all of these situations I try to smile back while walking (or while sitting if I'm sitting) and then continue on my way (or look the other way) but sometimes I feel like I want to get to know the random stranger too as they have expressed interest. To clarify, I'm talking about situations where it's more than just a quick glance and smile, but a prolonged one that may include other things too such as turning to face me. What can I do in order to do this successfully without it being awkward or intimidating the other person in the off case that they didn't want me to approach them, and also to befriend the individual in the process if they do?

edit: M/20

Answer 1

If you are standing close to the person, make a casual statement about the weather, or something about the public transport today, or some other totally benign topic. This gives the person who smiled at you a chance to react.

Be cautious as the person who seemed interested may have just been courteous. If they respond to your statement by grunting or smiling then looking away, then they don't actually want a conversation.

If they seem interested however, ask the person a question about themselves. It gives them another chance to decline the conversation, via giving you a short answer. If they are interested however, this gives them an opening into the conversation and you can take it from there.

Careful not to walk towards someone from a distance based on a small amount of eye contact and a smile however. This can be seen as threatening and intimidating and generally leaves a bad impression.