Pge 46 REVITION USE IN EUTIVE GEOMETR. Properties of Plne Geometry No. igrm Given ondition onlusion revition nd re djent 1 ngles on stright 180 dj. s on st. line line 2, nd re ngles t point 360 s t pt. 3 d O Two stright lines nd interest t point O nd d vert. opp. s 4(i) // orr. s, // 4(ii) = // orr. s equl 5(i) d // d lt. s, // 5(ii) d = d // lt. s equl 6(i) f e // e f 180 int. s, // 6(ii) f e e f 180 // int. s supp. 7 is 180 sum of 8 1 is 1 ext. of
Pge 47 No. igrm Given ondition onlusion revition 9 = = se s, isos. 10 = nd = = nd prop. of isos. 10 = nd = nd = prop. of isos. 10 = nd = nd = prop. of isos. 11 = = sides opp. equl s 12 = = = = = 60 o prop. of equil. 13 = = = = prop. of equil. 14 1 2 n 3 1, 2, 3, n re the interior ngles of n-sided onvex polygon 1 2 3 n 2 180... n sum of polygon 15 x 2 x 3 The sides of n n- x 1 x n sided onvex polygon re produed in order. x x x... x 360 1 2 3 n sum of ext. s of polygon
Pge 48 No. igrm Given ondition onlusion revition 16 = nd = nd = SSS 17 = nd = nd = SS 18 = nd = nd = S 19 = nd = nd = S 20 = nd = nd RHS = = 90 o 21 = nd = nd = orr. sides, s 22 = nd = nd = orr. s, s
Pge 49 No. igrm Given ondition onlusion revition 23 = nd = nd = ~ 24 ~ 3 sides prop. 25 nd = ~ rtio of 2 sides, in. 26 ~ orr. sides, s 27 ~ = nd = nd = orr. s, s 28 29 30 I I 31 I is I is the inentre of I is the entroid of I is the orthentre of + > + > + > I is the intersetion of the ngle isetors, i.e. = = = I is the intersetion of the medins, i.e. = = I I = I I I I 2 1 I is the intersetion of the ltitudes, i.e. inentre of entroid of orthoentre of
Pge 50 No. igrm Given ondition onlusion revition I is the intersetion of the perpendiulr isetors, i.e. I is the irumentre 32 I nd = irumentre of I of I nd = I nd = 33 is //grm = nd = opp. sides of //grm 34 is //grm = nd = opp. s of //grm 35 O is //grm nd O is the intersetion of digonls O = O nd O = O digs. of //grm 36 = nd = is //grm opp. sides equl 37 = nd = is //grm opp. s equl 38 O O = O nd O = O is //grm digs. iset eh other 39 = nd // is //grm opp. sides equl nd // 40 is retngle ll properties of //grm 41 is retngle ll the interior ngles re right ngles prop. of retngle 42 is retngle igonls re equl ( = )
Pge 51 No. igrm Given ondition onlusion revition 43 E is retngle igonls iset eh other into four equl prts (E = E = E = E) prop. of retngle 44 is squre ll properties of retngle 45 is squre ll sides re equl 46 is squre igonls re perpendiulr to eh other ( ) prop. of squre 47 is squre ngles etween eh digonl nd side is 45 o 48 is rhomus ll properties of //grm 49 is rhomus ll sides re equl 50 51 52 e f M d g h N is rhomus is rhomus M = M nd N = N igonls re perpendiulr to eh other ( ) Interior ngles re iseted y the digonls ( = = = d nd e = f = g = h) MN // nd 1 MN 2 prop. of rhomus mid-pt. thm.
Pge 52 No. igrm Given ondition onlusion revition 53 E F L 1 L 2 L 3 L 1 // L 2 // L 3 nd = E = EF interept thm. 54 M N M = M nd MN // N = N interept thm. 55 In, = 90 2 + 2 = 2 Pyth. thm. 56 In, 2 + 2 = 2 = 90 onverse of Pyth. thm. 57 E F is n isos. trpezium //, =, E = F, =, E = F, = EF, =, =. Nil / prop. of isos. trpezium 1 1 2 2 O d 2 58 is kite 2 1 d 1 =, =, =, 1 = 2, 1 = 2, 1 = d 1, 2 = d 2,, O = O. Nil / prop. of kite