Ivan used coordinate geometry to prove that quadrilateral EFGH is a square. Figure EFGH is shown. E is at negative 2, 3. F is at 1, 6. G is at 4, 3. H is at 1, 0. Statement Reason 1. Quadrilateral EFGH is at E (−2, 3), F (1, 6), G (4, 3), and H (1, 0) 1. Given 2.__?__ 2.segment EF E (−2, 3) F (1, 6) d equals the square root of the quantity 1 plus 2 all squared plus 6 minus 3 all squared d equals the square root of the quantity 3 squared plus 3 squared equals the square root of 18 equals 3 times the square root of 2 segment FG F (1, 6) G (4, 3) d equals the square root of the quantity 4 minus 1 all squared plus 3 minus 6 all squared d equals the square root of the quantity 3 squared plus negative 3 squared equals the square root of 18 equals 3 times the square root of 2 segment GH G (4, 3) H (1, 0) d equals the square root of the quantity 1 minus 4 all squared plus 0 minus 3 all squared d equals the square root of the quantity negative 3 squared plus negative 3 squared equals the square root of 18 equals 3 times the square root of 2 segment EH E (−2, 3) H (1, 0) d equals the square root of the quantity 1 plus 2 all squared plus 0 minus 3 all squared d equals the square root of the quantity 3 squared plus negative 3 squared equals the square root of 18 equals 3 times the square root of 2 3. segment EF is parallel to segment GH 3. segment EF E (−2, 3) F (1, 6) m equals 6 minus 3 over 1 plus 2 equals 3 over 3 equals 1 segment GH G (4, 3) H (1, 0) m equals 0 minus 3 over 1 minus 4 equals negative 3 over negative 3 equals 1 4. __?__ 4. segment EH E(−2, 3) H (1, 0) m equals 0 minus 3 over 1 plus 2 equals negative 3 over 3 equals negative 1 segment FG F (1, 6) G (4, 3) m equals 3 minus 6 over 4 minus 1 equals negative 3 over 3 equals negative 1 5. segment EF and segment GH are perpendicular to segment FG 5. The slope of segment EF and segment GHis 1. The slope of segment FG is −1. 6. __?__ 6. The slope of segment FG and segment EH is −1. The slope of segment GH is 1. 7. Quadrilateral EFGH is a square 7. All sides