This question came up in one of the posts in Blaine Bettinger’s Facebook Group Genetic Genealogy Tips & Techniques, so I thought I’d give a quick example here that I refer to myself when I get confused.

A man with 3 children, who have all tested, has a match to a 2nd cousin (documented through now through both DNA and traditional genealogy).  He and the 2nd cousin share 11 segments of DNA.

It so happens that all 11 of those segments have passed down to those 3 children, which you can see in the illustration below.  Of those 11 segments shared by their father and his 2nd cousin, Child 1 inherited 4 segments.  Child 2 also inherited 4 segments — but an entirely different four segments than Child 1.  Child 3 inherited 7 of the 11 segments.

The inheritance and sharing is illustrated below, in data pulled from GedMatch.

For purposes of illustration, we’re setting aside the fact that generally, when triangulating to find a common ancestor, we don’t use two full-blooded siblings as 2 of the triangle legs; they are too closely related, and will triangulate on many segments.

That said, Child 1, Child 2 and their 2nd cousin once removed (2C1R) have DNA in common with each other, but no triangulated segments with their 2C1R.  This is because Child 1 shares DNA with 2C1R on chr 6, on chr 12 and 2 segments on chr 15, while Child 2 shares DNA with 2C1R

Child 1, Child 3 and their 2C1R have 3 triangulated segments: on chr 6, on chr 12, and 1 segment of chr 15.

Child 2, Child 3 and their 2C1R also have 3 triangulated segments: on chr 4, on chr 8, and on chr 18.

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And that is a quick overview of triangulation vs. in common with.