It is easy to greet a stranger with just a smile and one word "HI". This will help the person know that you are willing to greet them and be friendly. Relationships begin with one person stepping out to invite the other person to join in the greeting and subsequent friendship. One gesture to a stranger is a smile only without the word "HI". This might prompt the person being given the smile to realize this is an approachable person to begin a daily or if not, a somewhat regular smile greeting each time they meet. A genuinely honest happy attitude with the smile will encourage most people to reciprocate.
Anytime a new person moves into the neighborhood, a wave at first will tell them you are a friendly person willing to greet them. As time goes by when they seem to have moved in, offer to share with them the places in the neighborhood they need to know about. When you go to the store ask if they would like you to take them along the first time so they can find their way by themselves. Invite them to church outings without the pressure to attend services. If they want more info they can ask the minister or you some other time.
If you were introduced into your new relationship's family members, you can recall how necessary a friendly approach was at that time. Include the person who is new to join in setting the table, pouring water into water glasses and any other part of the celebration they can help. If they seem awkward, assist them until they become more easily acclimated to what you think they can do to belong and feel included. If the kitchen is not their forte, ask them if they will get the door when someone else arrives. Show where the boots, jackets and purses are kept so they will know the routine.
Anyone who shows up to play a game of baseball does not necessarily know how to play all the positions. Invite the person to tell you their desire to learn which baseball position is what they wish to learn. Tennis is a game most people have to be well paired to play. Ask the new comber how long they have been playing tennis and let them play with you or someone else to find their niche. Board games are for everyone of a certain age. Don't expect a toddler to be able to play Canasta, but allow them to sit in with you to learn.
Greeting a new person in a budding relationship can be varied. AH, the advice about dates is a unique topic and one that there are so many angles to pursue. Take what you can use in this new relationship segment and form your own path for the relationships in the future for you and your family. First date should not be a formal one. A cup of tea, soda, ice cream cone or a short walk in the park or near water is good. This allows time to talk and see the connection between the two people. Some prefer double dating, at someone's home and this is something that can take pressure off the first date too.
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