Class-8

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cEof; v08 Class-8 tnsf jfSonfOk{ b ;ª\\ult ldnfO{ nv] M s_ d vfgf vfG5 . v_ cfdfn] uLt ufof] . u_ txF ¿ emu8f u5;{ \\ . 3_ alxgL ux[ sfo{ u5{ . ª_ pxfF sfd u5{ . r_ tkfO+{ ahf/ uof} . 5_ xfdLn] syf eGof] . lbg M 5kGg kf7 M kb;ªu\\ lt cWoog v08 cl3Nnf] lbgsf] tflnsf /fd|/L cWoog u/ . cEof; v08 != sf]i7sdf lbOPsf ;ªs\\ t] sf ;xfotfn] tnsf jfSo kl/jt{g u/ M s_ uf/] f s]6fx¿ cUnf klg 5g\\ . -Ps jrg_ v_ d]/f dfdfsf] 3/ ufpdF f 5 . -:qLlnªu\\ _ u_ d vN] b} lyPF . -tt[ Lo k?' if_ 3_ tF sfd u/\\ . -pRr cfb/_ ª_ r/fx¿ es\" Dk cfpbF f eml:sP/ p8]5g\\ . -Ps jrg_ r_ ;f9F ] 7'nf] / alnof] 5 . -:qLlnªu\\ _ 5_ n]lvsfn] /fdf| ] nv] n]lvg\\ . -k'lnª\\u_ h_ xfdL laxfg} p75\\ f}F . -Ps jrg_ em_ pgLx¿ es'G8f] v]N5g\\ . -Ps jr _ `_ ltdL lkª vN] 5f} . -:qLlnª_\\ @= sf]i7sdf lbOPsf ;ªs\\ t] sf cfwf/df tnsf jfSo kl/jt{g u/ M s_ ltdLx¿ kf]v/f k'us] f lyof} . -Ps jrg_ v_ pm gf6s vN] Yof] . -:qLlnªu\\ _ u_ xfdL ;dfh ;j] f ub}{ 5fF} . -låtLo k'?if_ 3_ cfdf vfgf ksfp5F . -kb ;ª\\ult_ ª_ 3f8] fx¿ af6fdf bub' {} 5g\\ . -Ps jrg_ r_ tF sf] xf];\\ < -k|yd k?' if_ 5_ 7n' L lbbL cfpg'eof] . -kl' nªu\\ _ h_ tkfO+{ d';'Ss xfF:gx' 'G5 . -cgfb/_ lbg M ;GtfpGg kf7 M afw] k|Zgsf] pQ/ cWoog v08 tnsf] cgR' 5]b Wofg lbP/ k9 . of] dn' 'sdf c;Lldt ;|ft] tyf ;fwgx¿ 5g\\ t/ klg ltgsf] pkof]u x'g g;s]/ b]z lg/Gt/ jb} l] zs C0fdf 8'Ab} uO/x]sf] 5 . oj' fju{ egs] f bz] kl/jt{gsf ;j+ fxs xg' \\ . /fi6« kl/jtg{ sf] d'Vo lhDdj] f/L ;l' Dkgk' g{] oj' fx¿sf xftdf kf;kf]6{ / le;f ydfP/ csf{sf] bz] df kl;gf aufpg afWo agfpg] ltg} /fhgLlts gt] fnfO{ kml] / klg bj] Tjs/0f u/]/ ltgs} k5fl8 nfUg' eg]sf] :jo+ cfkm\"kl| ts} ckdfg xf] . cfh klg ;/sf/ :jbz] d} /f]huf/sf cj;/ l;hg{ f ug]{ gLlt ;fjh{ lgs ub{} ljljw /fi6;« uF >d ;Demft} f --52--

Nepali u/L åw} rl/q k:| tt' ub{} oj' fx¿sf] laqmL ul//x]s} 5, Tof] klg sf}8Lsf] efpdf . ptf 3/ kl/jf/, Oi6ldq, ;fyL;ª\\uL / cfÇgf] z/L/ ;x' fpbF f] kof{j/0fLo cg's\"ntf;dt] Tofu]/ ljb]zdf cxf/] fq sl7g kl/>d ul//x]sf o'jfx¿nfO{ oxfFsf ;Qfwf/L / k|ltkIfdf /xs] f /fhgLlts bnsf gt] fx¿ ljleGg cj;/ / jfxgf kf/]/ lg/Gt/ nl' 6/xs] } 5g\\ . o'jfx¿sf] >d, ;do, ;DklQ, l;hg{ fTds Ifdtf / cfnf]rgfTds rt] gfdfly ;Lldt /fhgLlts bnsf gt] fx¿ ldnfO{ ldnfO{ lg/Gt/ n6' dRrfO/xs] } 5g\\ . cEof; v08 dflysf] cg'R5]b k9/] tnsf k\\Zgx¿sf] pQ/ b]pm M s_ b]z lg/Gt/ C0fdf 8'Ab} hfg'sf] sf/0f s] xf] < v_ oj' fx¿nfO{ s;n] kf;kf6] { / le;f ;dfpg afWo agfPsf] 5 < u_ oj' fx¿ sg' dN\" odf las|L eO/x]sf 5g\\ < 3_ sg' s'g s/' f n'6fpg o'jfx¿ afWo 5g\\ < ª_ /fh] uf/ / cxf]/fq zAbsf] cy{ n]v . lbg M cG7fpGg kf7 M Jofs/0f cWoog v08 tnsf] cg'R5]b cWoog u/ . xfd|f kv' f{n] xfd|f] ;+:s[lt lgdf0{ fdf 7\"nf] of]ubfg u/] . pgLx¿n] cfÇg} df}lns ;:+ s[lt lgdf{0fdf a9L hf]8 lbPsf 5g\\ . lrqsnf, d\"lts{ nf, jf:ts' nf Pjd\\ ;ª\\uLt / g[Todf klg gk] fnL df}lnstf emNsg] u/L ltgnfO{ lgdf{0f ul/Psf] 5 . pgLx¿ o; sfo{df /ftlbg v6y\\ ] . /fi6« / ;:+ sl[ tnfO{ dxfg\\ 7fGy] . cfh tL df}lnstf w]/} nf]k eO;s]5g\\ . ljleGg b/af/x¿, dlGb/x¿, dl\" t{x¿ tyf nfs] uLt / gT[ o o;sf kd| f0f xg' \\ . xfdLn] k'vf{af6 w]/} s'/f l;Sg ;S5fF} . kv' fx{ ¿ cfTdlge{/ lyP . xfdL lbglbg} k/lge{/ aGb} 5fF} . xfdLn] cfÇgf dxŒjk0\" f{ s/' f nTofP/ csfs{ f g/fd|f s/' fnfO{ cg;' /0f ul//x]sf 5f}F . of] s|d lg/Gt/ rln/xd] f xfdL k0\" f{tM k/lge{/ aGg]5f}F . xfd|f k/' ftflŒjs ;Dkbf / ;+:s[lt nf]k xb'F } hfg]5g\\ . xfdL kfgL l/lQPsf] ufuL| h:t} dfl} nstf x/fPsf] bz] sf gful/s ags] f x'g]5f}F . t;y{ xfdL cfh} ;rt] ag]/ kv' fs{ f bg] sf ¿kdf /x]sf ;+:s[lt / ;Dkbf hfu] fpglt/ nfuf}F . cEof; v08 dflysf] cgR' 5]bdf sfnsf ljleGg kIfsf ls|ofkbx¿ ko| fu] ePsf jfSox¿ 5g\\ . dflysf ;a} jfSonfO{ k0\" f{ et\" sfndf kl/jt{g u/L kg' n]v{ g u/. lbg M pgfG;f7L kf7 M JofVof cWoog v08 ;tF} L;fF} lbgsf] cWoog v08df xfdLn] nfdf] pQ/÷ljjr] gfTds pQ/af/] cWoog u/s] f lyof}F . To;nfO{ kg' M Psk6s x/] . cEof; v08 JofVof u/ M xs{ u'?ª g]kfnsf cdN\" o lglw xg' ,\\ s;/L < nfdf] pQ/ n]v . --53--

Class-8 lbg M ;f7L kf7 M j0fl{ jGof; cWoog v08 lk9F Ldf tf; v]Ngx] ¿ / cfuF gdf cg]s ukm xfFSg]x¿sf Ps Ps 8ˆkmf lyP . tL 8ˆkmfdf /xs] f tLg hgf a'hs|' x¿n] p;nfO{ b]v] . bfl} 8Fb} cfP/ ;DemfpFb} leq nu] . pm la:tf/} ;Dxflnof], p;nfO{ stfstf cK7]/f] dx;;' eof] . lk;fa km]g]{ afxgfdf zf}rfnolt/ uof] . kmsbF{ f p;sf] cg'xf/df ;ª\\sfr] / ;+zosf k|z:t /]vfx¿ bfl} 8/xs] f lyP . stf stf ef]s nfu]em}F eof] . Kof; 3fF6Lsf] ?b3| G6LeGbf klg dfly psfnf] nflu/xs] f] cfef; eof] . z/L/ o;/L yfs]emF} eof] ls dfgf}F pm lbge/ afn'jfsf af/] f afs] ]/ nDk6 k/s] f] 5 . t/ vf; p;nfO{ ePsf] rflxF s] lyof] < slt a]/ 3fl] /P/ ;fR] bf klg sx] L ep] kfpg ;sg] . cEof; v08 dflys]f cgR' 5]bdf rGblaGb' - F _ko| fu] ePsf zAb 5fg/] n]v . --54--

Subject : Mathematics Day - 1 (Angles) Activity Two angles are called adjacent angles if, a) They have a common vertex and common arm. b) Other arms of the angles lie on opposite sides of the common arm. Eg. P MO N ∡MOP&∡������������������������������������������������������������������������are adjacent angles in which ∡MOP + ∡PON = 180° Exercise b) D c) H Find the value of x&y. a) Z 3x x 45° A 2x x C +5 2x-25o XY B E oF G Day -2 WY Activity When two straight lines intersects each other at O a point, the angles so formed in opposite sides are called vertically apposite angles Eg. Here, ∡WOX&∡YOZ are V. O. A, they are equal to each other∡WOX&∡XOZare V. O. A, they are equal each other. Exercise XZ Find the value of a, b, c & d. cd a 90o a) ao b) 50o bo Day - 3 b 50o co Activity Look at the figure and find unknown angles. Here, ∡WXS = 4x°, ∡SXZ = 40°, ∡ZXY = 3x° ∡WXS + ∡SXZ + ∡ZXY = 180° Z S 40o 4xo 3xo W X Y --55--

Class-8  [Parts of angles on straight line is 180o] 4xo + 40o + 3xo = 180o or, 7xo + 40o = 180o or, 7x = 180 - 40 or, 7xo = 140o 140 or, x = 7 or, x = 20o  4x = 4 × 20 = 80o 3x = 3 × 20 = 60 Exercise D Find the angles of ao C A 90o 2a B 40o Day - 4 Activity a) Sum of complementary angles is 90o. b) Sum of supplementary angles is two right angles. (180o) Exercise a) If (x+10o) and (2x - 10o) are the complementary angles to each other find both angles. b) If (x +20)o and (3x - 40)o are supplementary to each other find both angles. Day - 5 C Activity From the figure, find the measure of ∡FBE. A 5x 3x B 3x 2x 2x F ED Here from given figure, ∡ABC + ∡CBD + ∡DBE + ∡EBF + ∡FBA = 360[Being angles by complete turn /circle) 5x+3x + 2x + 2x + 3x = 360o or, 15x = 360o or, x = 360 ° 15  x = 24o Now, ∡FBE = 2x = 2 × 24 = 48o Answer. --56--

Mathematics b) Exercise Find the value of a. 4a a) 3a 5a 4a 3a 3a 3a 5a Day - 6 Activity In the adjoining big lines MN & OP are parallel. ∡QSN & ∡������������������������������������������������������������������������, ∡������������������������������������������������������������������������ & ∡������������������������������������������������������������������������, ∡������������������������������������������������������������������������ ������������������������������������������������������������������������ & ∡������������������������������������������������������������������������, ∡������������������������������������������������������������������������ & ∡������������������������������������������������������������������������are corresponding angles, they are equal to each other. I Exercise 60o F H From the following figure find the value of a, b & c. E G ab C Day - 7 J E Activity G In the adjoin figure lines AB & CD are parallel M B to each other Now,∡AGH & ∡������������������������������������������������������������������������, ∡������������������������������������������������������������������������ & ∡������������������������������������������������������������������������ H D are alternate angle, they are equal to each other. C  Also study page - 8 (2.4) from your tent back. F Exercise b) 2a Find the value of x & a. a) 3a-10 x 5x 60o Day - 8 Activity  Study 2.5 & 2.6 (page - 9) from your text book.  Also revise activities 6 & 7. --57--

Class-8 Exercise b) B E F Find the value of a & b. a) C 40 a 120o Q AC bD 3a a D R Day - 9 Activities - From the given figure, find p, q, y & 2 60o 60o Here, po From the given figure, 60o+po+60o = 180o [parts of straight angles] or, po + 120o = 180o or, po = 60o zo yo 60o zo Again, qo + 60o = 180o[ Being W- interior angles and lines are parallel] or, q = 180 - 60o  q = 120o Now, q + y = 180o[ Sum of straight angles] 120o + y = 180 y = 60o Again, z = 120o 60 + z = 180 [ same as above]  P = 60, q = 120, y = 60, & z = 120o Exercise A Find the value of x, y & z 50 E Bz y 60o D C Day - 10 Activity Kindly request you to study example - 3 (page - 10) from your text book. Exercise A 35o B Find the value of x. Ex C 65o D --58--

FMinadththeme vaatliuces of x Day - 11 Activity Types of triangles on the basis of sides.  Equilateral triangle (All sides are equal)  Isosceles triangle (two sides are equal)  Scalene triangle (No sides are equal) Types of triangles on the basis of angles.  Right angled triangle (having one angle is 90o)  Acute - angled Triangle (having all three angles acute) Exercise  Draw 4 triangles of different shapes and sizes measure the size of sides and angles using ruler& protector than identify the types of triangle. Day - 12 Activity Kindly request you to study & follow the ideas given in experimental test - 1 (page - 15) from your text book. Exercise Verify experimentally that the sum of measures of interior angles of a triangle is 180o. (Draw two figures) Day - 13 Activity Kindly request you to study & follow the ideas given in experimental test - 2 (page - 15) from your text book. Exercise Verify experimentally that, the base angles of an isosceles triangle are equal. (Draw two figures) Day -14 Activity Kindly request you to study & follow the ideas given in experimental test - 4) (Page -16) from your text book. Exercise Verify experimentally that each angle of an equilateral triangle is 60o. (Two figures are enough) Day - 15 A Activity Find the measures of AB. 2x cm (x+ 3)cm --59-- 57 57 C B

Here, ∡������������������������ = ∡������������������������ = 57° Class-8 So, that AB = AC. P (x+ or, 2x = x + 3 62 5)cm or, 2x - x = 3 or, x = 3. R Now, AB = 2x = 2 ×3cm. = 6cm Exercise  Find the measures of PR Q 62 (2x-  Find the measures of base angles. A 70o BC Day - 16 Activity Kindly request you to study & write example - 1 (page - 17) from your text book. Exercise E Find the values of x, y & z 30 30 from the following figures. AB C D 120o yz x G E FH Day - 17 Activity Study the steps & method provided in example - 1 (page - 23) from your text book. Exercise  Construct the following regular pentagon. a) 5cm b) 6xm --60--