approving
Showing that you like or support something or someone.
Approving describes showing or feeling support, agreement, or satisfaction with something or someone. When your teacher gives you an approving nod after you answer a question well, she's showing that she's pleased with your response. When parents exchange approving glances as their child performs in the school play, they're silently communicating their pride and support.
An approving look, smile, or comment signals that someone thinks what you're doing is good or right. This matters because approval from others, especially people we respect, helps us know we're on the right track. A coach's approving pat on the back tells a player their effort is noticed. A friend's approving reaction to your art project encourages you to keep creating.
Someone with an approving attitude toward your plans supports what you're trying to do. Notice that approving is different from simply agreeing: it carries a sense of positive judgment, like when a librarian gives an approving smile as you check out a challenging book, showing she thinks it's a good choice for you.