1. Emma that f : IEIE2 _3. E3 is an issmstrgr sf ths plans. Shaw that: {a} if f has tars pints a and h sf the plans. than I is a rssstisn I'Ellati'lul'E ts the ns dstsrmiILsd by a and h; {h} if f xss a unique paint :1. than 3' is a rotation arsund a; [s] if 3' rms rust x any point, than I is a translatisn, fsllswsd passiny by a rstatinn andfnr a rssctinn. E. Cansluds the prnnf sf Pmpn-sitin 1.3.3. 3. Gsnsluds the pmnf [if Prupnsitin 1.3.5. 4. Shaw that ths Klsih grnup is isomorphic ts E; 3 g. 5. Shaw that the fallow-ring ssts sf transfsrmatisns are groups: {a} Ths arthsgsaal transfsrmatishs and prspsr ratatisas f : IE" _3. IR\". {1:} Ths issmstriss f rIFE.\" _1. R". [s] Ths symmstriss of a gure it C IR\". IE. Shaw that the spacial shsgsnal gruup SUE-a, IR} is a annual subgmup sf Dlzn}. but it is nut a nnrmal subgmupnf Em, IE1}