Sherry, you're using a visualization option following a One-to-Many search. That will not give you valid results for this purpose because it doesn't perform complete segment triangulation. You're not comparing everyone in the hypothetical triangulation group to everyone else based upon cross-matched segments.
Go to either the regular or Tier 1 One-to-One matching tools and compare A589040 and M648925:
Comparing Kit A589040 (____) [Migration - F2 - A] and Kit M648925 (____) [Migration - V4 - M]
Segment threshold size will be adjusted dynamically between 200 and 400 SNPs
Minimum segment cM to be included in total = 7.0 cM
No shared DNA segments found
Those two kits have no meaningful DNA in common. You would need to drop down to 4cM or below to find any tiny segments that they might share, and none of those are on Chr 10.
If you want a real-world example of why tiny segments can't be used, try running a Q Matching One-to-One of your kit against mine, QJ297469C1, with the threshold lowered to 3cM. I'm sure we can agree that our family trees give no indication at all that we should share 65.4 cM across 18 segments. These are all either false segments, testing artifacts, or are IBS-only as a result of very deep population-level ancestry that can't be applied genealogically.
If you want to use the GEDmatch segment triangulation tool, it's under Tier 1, "Triangulation." You enter only one kit number, so use yours. Choose only Chromosome 10, and select "Cross-match triangulated segments with others within chromosome." You can leave everything else at the default values.
Because the starting locus of all the matches we're talking about is near the telomere, at the end of the chromosome, the calculated triangulation group will be shown at the end of the first section.
I'm including only the kit numbers, not the names, but the individuals who are in TG10_8 Chr 10 are:
Triangulated Group Names:
kit: A164431 Name: ____
kit: A589040 Name: ____
kit: HZ4084826 Name: ____
kit: M012661 Name: ____
kit: M814622 Name: ____
kit: RL5365418 Name: ____
kit: SY1898734 Name: ____
So not appearing in the triangulation group are M648925 and A386617. I personally never rely solely on the "GEDmatch Segment Triangulation" report without building a one-to-one matching matrix myself in order to better understand how everyone involved compares to everyone else.
Also, as popular genetic genealogist Jim Bartlett reinforces over and over, we shouldn't think of triangulating people, but segments. Sometimes you might want to subdivide a triangulation group further because, even though everyone in the TG might share a segment, it might only be only a small segment...since we have to look for the lowest common denominator. For example, if I match you from 10 to 200, and my cousin Whozzat matches me from 10 to 900, but matches you at 198 to 700, then our in-common, mutually-shared segment is only 198-200...because that's the only small bit we all share with each other.
I wanted to avoid adding this, but I feel it's sorta necessary now, all things considered. There is still no scientific, peer-reviewed research that indicates our method of triangulation of distant cousins for genealogy with our popular microarray tests has any validity. Intuitively, it would seem it should work for relatively close cousins, but there are several reasons it should not work for distant cousins. The simple biological mechanisms of meiosis and independent assortment greatly stack the odds against it functioning as many believe it does...at least if we're talking about descendancy-identifiable data and not merely exonic or continental population-level SNPs.
For the very same reason that no two siblings have the same DNA (other than monozygotic twins)--even if the couple has 20 children--the odds of any three distant cousins sharing any measurable-via-microarray DNA quickly becomes astronomical. For example, when AncestryDNA still used DNA Circles and calculated down to 5cMs (they now use 8cM), their Help paper on the subject said:
Our research shows that the chances that three first cousins will all have the same matching segment (in this case one that is at least 5 cM long) is about 85 percent; three third cousins have only a 15 percent chance. And the chance that three fourth cousins will all share the same matching segment is practically zero.
The emphasis is mine. And, mind you, Ancestry was talking about the available data after they had scrubbed the matches using the BEAGLE and Timber algorithms. I've been hoping for quite some time to see solid research that would simulate the DNA inheritance conundrum triangulation of distant cousins presents, but I take Ancestry's stance actually to be on the optimistic end of the spectrum.
If we were to apply the same, simple probability calculation of three mutually independent events--like rolling three dice and having them all come up on the same number--and apply it to data like we see in an important paper that evaluated real data from 23andMe (Henn, et al. PLoS One, 2012), we'd see that the probability of three 5th cousins sharing a genealogically meaningful matching segment would be 0.003308; for 6th cousins it would be 0.000069. If we could effectively do simulations I have a feeling the results wouldn't be quite that low, but they would still be very low...as in highly improbable any three 5th cousins or greater would share a meaningful matching segment. And it wouldn't matter if the individuals were absolutely correct in the family tree or not. The way our biology is engineered for genetic diversity simply shouldn't allow it to happen very often at all.
We have generally accepted guidelines here and elsewhere for autosomal triangulation of distant cousins, but for the purposes of your own research with a goal toward accuracy, this is just a parking-lot notation that nobody knows if it actually works, if it actually reveals any valid genealogical information.
