Dogs, unlike humans, do not point (unless trained to do so). When a dog extends his paw, he is not trying to show you something across the room but is more likely looking for some sort of attention, or displaying a behavior that usually generates a positive response.
If your dog has been trained to shake or perform high fives, an extended paw could simply be him trying to earn a bit of positive attention with a behavior that usually generates such results. Dogs love positive attention and will often run through whatever behaviors they can think of to inspire you to deliver it. If your dog is sitting up and attempting to shake, this is the likely explanation.
Many dogs enjoy a good belly rub or chest scratch. If your dog is a fan of physical affection, placing his paw on your knee or extending it while lying down could be a simple request to you to give him scratches in his favorite spots. Extending a paw exposes parts of the dog’s chest and underarms, making it easy for you to hit the hard-to-reach places.
Some dogs enjoy physical contact like snuggling or cuddling. Affectionate dogs may extend their paws just to be in contact with their owners. If your dog regularly places his paws over your feet or touches you while you are both relaxing, chances are good he is just trying to stay close (or warm). Dogs often reflect the physical affection of their owners—non-snugglers may end up with more aloof pups.
An enthusiastic shake or a big bow with two paws extended in front is usually indicative of one thing: it’s playtime. Some dogs are paw-ier than others and will extend their paws as normal parts of their physical play; play bows are very positive indicators of a dog’s comfort level and readiness to play. When your pup is wagging his tail and pawing at you, he may be in the mood for a romp.
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