The right sign for branch is going to depend on what kind of branch
you are referring to.
BRANCH (Version: A branch extending from a tree.)
One approach is to do the sign for "TREE" with your non-dominant
hand (and keep it in the air) as you hold the index finger of your
dominant hand alongside one of the fingers of the non-dominant hand
and move the dominant index finger outward from the tree as if
showing how the "branch" extends from the "tree."
BRANCH (Version: Use "C" hands to depict the size and shape of a
branch off of a tree: "A
large tree branch.")



BRANCH-off-from:
English uses the word "branch" in various ways. If you use the
phrase "branch off of" or "branch off from" it means "diverge" or
split off.
To sign DIVERGE, you hold both index fingers (palm down) in front of
you. Then slide your dominant index finger forward and veer it off
to the side (sort of like an "exit ramp" veering off from a highway.
(Keep the non-dominant hand still).
Also see:
TREE
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American Sign Language (ASL) online at American Sign Language University ™
ASL resources by Lifeprint.com © Dr. William Vicars