Answer:
1 . I really trusted jack but he lies to me about his grades and __let me down.
2.Helen is my best friend.we like doing things because we __we have lot in common.
3.Both my brother and I are __keen on playing chess. we really enjoy it.
4. I __ fancied kate the first time I saw her. She is a really nice person.
5. I am new here and I need some time to __ get to know the people.
6. Tom and Tina live in different countries but they are good friends because they __get in touch every weekend.