They did? I've never seen one eat, nor what they preferred for food before the Flood.
Here's what the Word says. Read it and be informed. Before the Flood, for a period of more than a thousand years, this prevailed:
Genesis 1:28-30 (AV):
28 And God blessed them, and God said unto them, Be fruitful, and multiply, and replenish the earth, and subdue it: and have dominion over the fish of the sea, and over the fowl of the air, and over every living thing that moveth upon the earth.
29 And God said, Behold, I have given you every herb bearing seed, which is upon the face of all the earth, and every tree, in the which is the fruit of a tree yielding seed; to you it shall be for meat*.
30 And to every beast of the earth, and to every fowl of the air, and to every thing that creepeth upon the earth, wherein there is life, I have given every green herb for meat*: and it was so.
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(Note: * = meat here in Elizabethean English, "meat" simply meant "food." In this passage it does not refer to flesh meat.)
But after the Flood, right when Noah and the world of living creatures dismounted from tha Ark (including one wold expect, young dinosaurs), God changed the diet of humans, and probably some animals as well:
Genesis 9:1-3 (AV):
1 And God blessed Noah and his sons, and said unto them, Be fruitful, and multiply, and replenish the earth.
2 And the fear of you and the dread of you shall be upon every beast of the earth, and upon every fowl of the air, upon all that moveth upon the earth, and upon all the fishes of the sea; into your hand are they delivered.
3 Every moving thing that liveth shall be meat* for you; even as the green herb have I given you all things.
Actually, the dental professor and Creationist lecturer Dr. Jobe Martin has noted that the roots of the tyrannosaurus rex dinosaur are not rooted deeply enough nor strong enough to tear flesh. But they are sharp enough to strip leaves cleanly for the TR to eat, or maybe into decayed flesh like the hyenas. I doubt that the dinosaurs were able to survive the change in climate, even before the Ice Age.
So I think the Bible tells me that tigers began to eat flesh meat after the Flood, first maybe animals that died and were easier for aged tigers or beetles to eat, then maybe hunting live animals in the time when the weather turned wintry after the flood (which apparently it was not before the fountains of the deep were opened up by the cracking of plates into the continents).
Which chapter tells of the ice age?