In 1790 Gideon lived in Dorchester, New Hampshire.  By 1850 he was living in Cherry Valley, Ohio with his wife and three others, likely children or relatives. 
Household Role Sex Age Birthplace
Gideon Bridgman Male 62 New Hampshire
Elizabeth S Bridgman Female 62 Massachusetts
Eunice B Bridgman Female 28 Ohio
Thomas B Bridgman Male 19 Ohio
Daniel G Bridgman Male 38 New Hampshire
Gideon Bridgeman and Betsy I. Barker were married in 1810 in Dorchester, New Hampshire. 
↑ "United States Census, 1790," database with images, FamilySearch (https://familysearch.org/ark:/61903/1:1:XHKY-LC1 : accessed 9 April 2019), Gideon Bridgeman, Dorchester, Grafton, New Hampshire, United States; citing p. 21, NARA microfilm publication M637, (Washington D.C.: National Archives and Records Administration, n.d.), roll 5; FHL microfilm 568,145.
↑ "United States Census, 1850," database with images, FamilySearch (https://familysearch.org/ark:/61903/1:1:MXSR-43Y : 12 April 2016), Gideon Bridgman, Cherry Valley, Ashtabula, Ohio, United States; citing family 2252, NARA microfilm publication M432 (Washington, D.C.: National Archives and Records Administration, n.d.).
"New Hampshire Birth Records, Early to 1900," database with images, FamilySearch (https://familysearch.org/ark:/61903/1:1:FLLQ-H9H : 10 March 2018), Gideon Bridgman in entry for Hannah B Bridgman, 20 Dec 1810; citing Dorchester, Grafton, New Hampshire, United States, Bureau of Vital Records and Health Statistics, Concord; FHL microfilm 1,000,485.
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It may be possible to confirm family relationships with Gideon by comparing test results with other carriers of his Y-chromosome or his mother's mitochondrial DNA.
However, there are no known yDNA or mtDNA test-takers in his direct paternal or maternal line.
It is likely that these autosomal DNA test-takers will share some percentage of DNA with Gideon: