3 = 90 - = 5 80 - = 57 5 3 3 3 = 90 = 67 5 3

AN DE M DM BN ABN DM BN BN OE = AD OF = AB OE= AD=AF OF= AB=AE A= 90 AE=AF

30 BF BE BF= BE= a+b =a+ b BF=BC+CF=a+CF CF= b CD=b FD= b

AD= FC DFC DM= FC AD=DM 3= 4

AD AE = DB EC DB AD EC AE AB AC AB AC = = DB EC AD AE AD AE = AC = DE AD AE 39 ED BC = BC AC = DE AB AB BC BM AB = BM = AB CD ACE BN AE CD AC AC BN BC = BN = AE BC BM = BN AE AC AC AF BD AC F = FC BC BD GD BD AF AF AE = = 4 CG AD = = BC FC BC FC FC GC ED BD = GC BC

NF CF = AF NFC AFM FM

AC F AF = FC EF = 3 BE FC FC FC

AF AE AFE ADB = AF AB = AE A AD AB

AB BD = CE = AC tg α = AD tg α = FD ctgα tgα cosα cosα = GH = GB cos α = GB cosα cosα

AB AE = AB AD AE AC AD AC

AE FA = EC FB F EF = 3 BE ABC VA= 60 a+b+c= 0cm S = 0 3cm S = b c sin A bc = 40 ABC 0 S ABC= b h b, S ABC= r a+b+c r= cm 3 ABC

MD BD = BA = FC FE = FB FE = CM AE = CE AE CE MD = CM

77 AD+BC=AB+CD=a+b a+b CE AB E CE= a+b sinα O BE CF PQ = 4 BC r x + y r r r - 3 r + 3 4r

BD= BC ADC DCA= 90 DC = BC = AC BC AC =

AB AC =AB AD AC = AC A B AD AEB = D + C AFC = D - B AEB ABE AEB= 80 - - 3= 80 - A B= 80 - A+ B A+ B 360 - C- D AFG= 80 - - 7= 80 - A- C+ B A + C

BD = AE DC AF CE AE = 64 8 cm AD = 7 7 cm

9 O AB = AD B O DA C CE AB E BE = DC BA F BF = BE EF = BE = BF BF = DC BE = BE = DC AB= AD = = 3 EF=BE

AM AN MN BC = AB AC AM AB = NE BD AN AC AN AD = AE AN AB AB AM AE = DAM CAE AD AC AM AD MDA = ECA DM EC = AE AC AH = GK GK BC GK = BC AH = BC

BD =AC = = BD PB = CD PA DB DE = PB BD PA CD = BD DE DB = BD DE = PB PA

AB ABD AEB AE = AD AB =AD AE AB

AB = AB = BED AEC BE AE = ED EC

CA CA R O R O R = R, = sin sin AD AD R, = R, = R R = R R sin sin AB C OB D B = 3 AC CD

BD PB = CD PA BD BP = BD = BE BP CD = BE BA BA DP OD CD = DP OD BD DB DB CD C BD O PA AD = BO AC PA PA PA AD

PA AD CO PA OC AC = AC PC = OA OC AC = PA PA = OA AC PC = PO PA = PA OC BC = PO AB = OB OA OA AD BD AD AC = AB PC = BD AD AB = PA PA = BD AO PO ABC BC=a AC=b AB=c s= a+b+c ABC = s(s - a)(s - b)(s - c) 3 m = a + c - b a 4 ha, h = c - m a a + c - b 5 m h a = c - a 6 h = c - (a + c - b ) a ( a) 4a c - (a + c - b ) 7 h a = 4a (ac + a + c - b )(ac - a - c + b ) 8 h a = 4a [(a + c) - b ][b - (a - c) ] 9 h a = 4a (a + c + b)(a + c - b)(b + a - c)(b - a + c) 0 h a = 4a

s(s- b)(s - c)(s - a) h a = 4a 4s(s - a)(s - b)(s- c) = a ha = s( s a)( s b)( s c) a 3 S = ABC a ha = s(s- a)(s- b)(s - c) AB BC = AD CD

BM MC = AB AC AG AE GAE= HAC AHC AGE AG=AC AE AH= AG AC BCH AM HC BM MC = BA AH AE BM MC AB AG AC = AB AC = AE AG AE

AB AF = BG FC = BG FC = BP PBA QFA FQ AB BG = FC = BG = BP ABP AF FC FQ

OD Rt DOC OC = BD AC = 3 4 BC = cm AC = 6cm S = = 96cm p x + y =, x + y = m x + y = P 4 x + y - xy = P 3 4

x + y = m (4) m 4 3 - xy = P 4 xy = m - P 4 4 S = AC BD = x y ABCD = xy = m - P 4 O AED O E D = BC = 3 AB AE 3

AF = x AB = 3 3 3 3 + 3 AE + AE - 4 3 3 3 = 0 AE = 3 - S = AD DE BCD BC DG DE BC ADE ABC = AB BC BC = AB DE DG DB AF DB DBG ADF = DG = AD AF AD AD S = AB DE AF DB BCD AD AD AB DE AF DB DE AF = AD AD = AB DB AD + 0AD- 00 = 0 AD = -0 +0 3 S ADF = AD AB 4-3 S ABC (-0 + 0 3) = = 4-3 S S = ADE ABC EO=OF EO=OF=x x = AC -x CO x = AO CO BD BO = 9 DO x BO = 9 -x BO x DO = x 9 x -x x = x 36 7 x= 08 x=, EF= x= 9 x 7 7

AB 0 CD 90 S AMB S CMD 00cm AB CD ADB = 60 DA = 45 DM AM DM S DMC = = = sin 45 sin60 AM 3 S 3 AMB S = 40cm S = 60cm DMC AMB M N BE F AC G H MN = EF = GH = 90 BC OD AD AD 3 3 3 a a OD a OD EF 6 EF EF 90 EOF = 90 EOD = 6 πoe πa 45 OE = OD = a S = = S = a OEF DOF 6 4 4 a a a a a S = - S = - 3-4 6 4 ) = a a EmF - 6 8 + 3a = 4 a - 3 a + 6a + 6 a 4 4 F OC = OF OE OC = 7 93cm CD = AC CB CD = (89-7 93) 89 + 7 93 CD = 38cm BP = 0-5 3 AP = 5 6-5