Yes, the freshwater angelfish is a cichlid. They belong to the genus Pterophyllum and are endemic to various locations in the Amazon basin of South America. Many aquarists don't realize that these thin, oddly shaped, "finny" fish are cichlids, though they are very popular in the hobby. I personally have never kept them, so can offer nothing substantive about them. However, they are readily available at most fish stores.
Because of their popularity in the hobby, there are numerous resources available to learn about them, if you've never kept them or are a novice cichlidophile. One good place to start is this article in Tropical Fish Hobbyist.
The Cichlid Room Companion
Tropical Fish Hobbyist
American Cichlid Assoc.
African Cichlid Hub