In　this　paper,　periodic　event-triggered　leaderless　and　leader-following　consensus　problems　are　studied　for　linear　multi-agent　systems　with　deterministic　packet　losses　under　the　generic　directed　communication　topology.　Specially,　an　event-triggered　mechanism　is　proposed,　which　only　needs　to　communicate　the　event-triggered　states　of　the　agent　and　verify　the　event-triggered　condition　at　the　periodic　sampling　instants.　A　switched　system　with　stable　and　unstable　subsystems　is　used　to　describe　packet　dropouts　in　a　deterministic　way.　The　incidence　matrix　of　a　directed　spanning　tree　in　the　directed　communication　topology　is　utilized　to　construct　a　linear　transformation　so　that　the　consensus　problems　are　equivalently　transformed　into　the　asymptotic　stability　problems　of　reduced-order　systems.　Then,　some　sufficient　consensus　conditions　are　derived　and　the　consensus　protocol　gains　are　designed.　Finally,　simulation　examples　are　given　to　show　the　effectiveness　of　the　proposed　results.