Feeding street animals:
One is not obligated to feed his friends pets or street animals from his own food. [This applies even if the animal is endangered and may die.] Nevertheless, it is proper to give a stray dog a small morsel of food in order to emulate Hashem’s ways of mercy. One is to then hit the dog with a stick after throwing it the food in order to discourage it from returning back.
One is not Halachically required to feed stray animals from his own food/money, although it is proper to give some food to a dog on a one-time occasion.
Why does the Torah not obligate one to feed stray and helpless animals?
Various reasons can be attributed for why we do not find an obligation in this matter.
a) The Torah does not intervene on all matters, and leaves certain areas to the jurisdiction of man to decide. The same way there is no law in the United states that forces civilians to feed stray animals, so too, Lehavdil, such a law does not exist in the Torah, even though it is agreed upon in all societies that it is an act of kindness and mercy to do so.
b) Most stray animals have their own way of achieving a source of food, and by people feeding them it invites the animals into the neighborhood, and can become a nuisance for others.
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 Admur Hilchos Ovrei Derachim 3; Bava Metzia 88b
The reason: As the Torah did not obligate due to Tzaar Baalei Chaim for one to spend his own money to help animals, and he is only obligated to place bodily effort in saving them. [Admur ibid]
 Admur in Kuntrus Achron 3
 Admur ibid; Admur 324/7; Shabbos 155b
How Hashem shows mercy to the dogs: Hashem shows mercy to dogs by having the food stay in their abdomen for 72 hours, being that its food is scarce. [Admur ibid]
 Admur ibid; Shabbos ibid