We measure the branching fractions and CP asymmetries for the singly Cabibbo-suppressed decays D0 → π+π−η, D0 → K+K−η, and D0 → ϕη, using 980 fb−1 of data from the Belle experiment at the KEKB e+e− collider. We obtainBD0→π+π−η=1.22±0.02stat±0.02syst±0.03Bref×10−3,BD0→K+K−η=1.80−0.06+0.07stat±0.04syst±0.05Bref×10−4,BD0→ϕη=1.84±0.09stat±0.06syst±0.05Bref×10−4,\\documentclass[12pt]{minimal}\t\t\t\t\\usepackage{amsmath}\t\t\t\t\\usepackage{wasysym}\t\t\t\t\\usepackage{amsfonts}\t\t\t\t\\usepackage{amssymb}\t\t\t\t\\usepackage{amsbsy}\t\t\t\t\\usepackage{mathrsfs}\t\t\t\t\\usepackage{upgreek}\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\t\t\t\t\\begin{document}$$ {\\displaystyle \\begin{array}{c}\\mathcal{B}\\left({D}^0\\to {\\pi}^{+}{\\pi}^{-}\\eta \\right)=\\left[1.22\\pm 0.02\\left(\\mathrm{stat}\\right)\\pm 0.02\\left(\\mathrm{syst}\\right)\\pm 0.03\\left({\\mathcal{B}}_{\\mathrm{ref}}\\right)\\right]\\times {10}^{-3},\\\\ {}\\mathcal{B}\\left({D}^0\\to {K}^{+}{K}^{-}\\eta \\right)=\\left[{1.80}_{-0.06}^{+0.07}\\left(\\mathrm{stat}\\right)\\pm 0.04\\left(\\mathrm{syst}\\right)\\pm 0.05\\left({\\mathcal{B}}_{\\mathrm{ref}}\\right)\\right]\\times {10}^{-4},\\\\ {}\\mathcal{B}\\left({D}^0\\to \\phi \\eta \\right)=\\left[1.84\\pm 0.09\\left(\\mathrm{stat}\\right)\\pm 0.06\\left(\\mathrm{syst}\\right)\\pm 0.05\\left({\\mathcal{B}}_{\\mathrm{ref}}\\right)\\right]\\times {10}^{-4},\\end{array}} $$\\end{document}where the third uncertainty ( mathcal{B} ref) is from the uncertainty in the branching fraction of the reference mode D0 → K−π+η. The color-suppressed decay D0 → ϕη is observed for the first time, with very high significance. The results for the CP asymmetries areACPD0π+π−η=0.9±1.2stat±0.5syst%,ACPD0→K+K−η=−1.4±3.3stat±1.1syst%,ACPD0→ϕη=−1.9±4.4stat±0.6syst%.\\documentclass[12pt]{minimal}\t\t\t\t\\usepackage{amsmath}\t\t\t\t\\usepackage{wasysym}\t\t\t\t\\usepackage{amsfonts}\t\t\t\t\\usepackage{amssymb}\t\t\t\t\\usepackage{amsbsy}\t\t\t\t\\usepackage{mathrsfs}\t\t\t\t\\usepackage{upgreek}\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\t\t\t\t\\begin{document}$$ {\\displaystyle \\begin{array}{c}{A}_{CP}\\left({D}^0\\ {\\pi}^{+}{\\pi}^{-}\\eta \\right)=\\left[0.9\\pm 1.2\\left(\\mathrm{stat}\\right)\\pm 0.5\\left(\\mathrm{syst}\\right)\\right]\\%,\\\\ {}{A}_{CP}\\left({D}^0\\to {K}^{+}{K}^{-}\\eta \\right)=\\left[-1.4\\pm 3.3\\left(\\mathrm{stat}\\right)\\pm 1.1\\left(\\mathrm{syst}\\right)\\right]\\%,\\\\ {} ACP\\ \\left({D}^0\\to \\phi \\eta \\right)=\\left[-1.9\\pm 4.4\\left(\\mathrm{stat}\\right)\\pm 0.6\\left(\\mathrm{syst}\\right)\\right]\\%.\\end{array}} $$\\end{document}The results for D0 → π+π−η are a significant improvement over previous results. The branching fraction and ACP results for D0 → K+K−η, and the ACP result for D0 → ϕη, are the first such measurements. No evidence for CP violation is found in any of these decays.