Which observations led darwin to establish a relationship between extinct and living animals?

Darwin discovered that the fossilized remains of giant sloths were found in places where smaller sloths now live. While there is a similarity between The bony shells of armadillos and the shells of ancient Glyptodon fossils.

Darwin was pondering over why he found fossils of extinct animals in the places where he found also the similar, living animals. In the end, these observations reinforce his idea that today's living species descend from older, extinct species.