That is not how cladistics works when classifying the relationships between organisms. In cladistics, organisms are classified into groups (clades) based on their shared evolutionary lineages (i.e. all organisms that share a most recent common ancestor are placed into a single clade).
Following this, birds and dinosaurs are within their own clade Dionsauria, since birds are derived from theropod dinosaurs. Dinosauria is then nested within the larger clade Archosauria, which includes everything in Dinosauria, along with Pterosaurs and everything within the clade Pseudosuchia (crocodiles and their relatives), since they all last shared a common ancestor some time in the late Permian or early Triassic. This is why the closest living relatives to birds are currently crocodylians. Keep stepping back further and further like this through and you can then classify all reptiles into a single clade (see the image below for a simplified version sourced from:
http://www.ucl.ac.uk/museums-static/obl4he/vertebratediversity/). Hence under cladistics, dinosaurs and birds are reptiles. Following this we are all also technically just highly derived fish!
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This is the simple version of how reptiles are classified within the tree of life. Currently depending on the phylogeny you look at, reptiles do not form a monophyletic grouping (group consisting of all descendants from a common ancestor) depending on where turtles and tortoises actually sit within the tree of life, but that is a bit complex for now (and currently unresolved).
Hopefully this all makes sense and clears up where birds, dinosaurs and reptiles actually sit next to each other. Have to admit though, this is a massive side track from what this post started as!
Cheers, Cameron