tharindu hasange. (bsc in computer engineering) dharmaraja … › pms › content › downlord ›...

Prepared By :- Tharindu HaSange. (Bsc in Computer Engineering) Dharmaraja Maha Pirivena - Nedalagamuwa

Prepared By :- Tharindu HaSange. (Bsc in Computer Engineering) Dharmaraja Maha Pirivena - Nedalagamuwa

1. ,CIhlg iu ÿßka msysá m:h jD;a;h fõ

wrh 3.5 cm jk jD;a;la ks¾udKh lrkak

^id'fm<& 2006 foieïn¾

i. AB = 6 cm o A ̂C = 900 o BC = 4 cm o jk ABC ;%sfldaKh ks¾udKh lrkak

ii. D ys§ AB yuqjk mßÈ A ̂B iuÉfþokh ks¾udKh lrkak

iii. D flakaøho BD wrho jk jD;a;h ks¾udKh lrkak

iv. A isg jD;a;hg weÈh yels AE yd AF iam¾Il fol ks¾udKh lrkak

v. ABC ;%sfldaKh ioyd mhs;.ria m%fïh fh§fuka AC ys È. √ weiqßka ,shkak

vi.

vii. AC ys È. uek ta weiqfrka √ ys w.h oYuia:dk tllg ,nd .kak

AED ;%sfldaKfha j¾.M,h = √ - 1 nj fmkajkak

BCD ;%sfldaKfha j¾.M,h 2


i. wrh 4 cm yd flakaøh C jQ jD;a;hla ks¾udKh lrkak

ii. tu jD;a;fha 6 cm È. AB cHdhla ks¾udKh lrkak

iii. AB ys ,ïN iuÉfþolh ks¾udKh lr th jD;a;h fþokh lrk

,CIh D f,i kï lrkak

iv. D ys§ jD;a;hg iam¾Ilhla ks¾udKh lrkak

v. A ̂D fldaKfha iuÉfþolh ks¾udKh lr ty by; iam¾Ilh

fþokh lrk ,CIh P hehs kï lrkak

vi. PA hd lr PAC PCD nj idOkh lrkak

vii. PA f¾Ldj A ys§ jD;a;h iam¾I lrk nj fmkajkak

viii. PC ys È. uek ,shkak

ix. by; (viii) ys ms<s;=r weiqßka P,A,C yd D ,CIH yryd hk jD;a;fha wrh fidhkak

2. ,CIh 2lg iu ÿßka msysá m:h tu ,CI fol hd lrk f¾Ldfõ ,ïN iuÉfþolhhs

1st. 5 cm È. f¾Ldjla wÈkak

2nd. f¾Ldfõ fl,jrl ljlgqfõ ;=v ;nd f¾Ldfõ fomi pdm folla f¾Ldj ndysrfhka ks¾udKh lrkak

3rd. f¾Ldfõ wfkla mi ljlgqj ;nd weÈ pdm fþokh jk f,i ;j;a pdm folla ks¾udKh lrkak

4th. pdm fþok ,CI hd lrkak

3. f¾Ldjl msysá ,CIhl§ tu f¾Ldjg ,ïNhla ks¾udKh 1. f¾Ldjla u; P kï ,CIhla msysgqjkak

2. ljlgqj P u; ;nd f¾Ldj fomi f¾Ldj u; pdm folla ks¾udKh lrkak

3. tu pdm fol u; ljlgqj ;nd f¾Ldj ndysrfhka fþokh jk f,i pdm folla ks¾udKh lrkak

4. pdm fþok ,CIh yd P hd lrkak


i. 9 cm È. AB f¾Ld LKavh wÈkak

ii. AB ys ,ïN iuÉfþolh ks¾udKh lrkak th AB fþokh lrk ,CIh

O f,i kï lrkak

iii. O flakaøh jQ o AB úIalïNh jQ jD;a;h ks¾udKh lrkak

iv. AC = 7 cm jk fia jD;a;h u; C ,CIhla ,l=Kq lr ABC ;%sfldaKh wÈkak

v. OC hd lr C ys§ jD;a;hg iam¾Ilhla ks¾udKh lrkak

^id'fm<& 2008 foieïn¾ úfYaI m;%h ^kj ks¾foaYh&

i. BC = 9 cm , C ̂A = 600 yd BA = 4.5 cm jk ABC ;%sfldaKh ks¾udKh lrkak

ii. BC mdofha uOH ,CIh jk L ysÈ jD;a;h iam¾I lrkakd jQ o flakaøh

AC u; msysgkakd jQ o jD;a;h ks¾udKh lrkak tys flakaøh O hehs kï lrkak

iii. CL yer C isg jD;a;hg weÈ wfkla iam¾Ilh ks¾udKh lr P kï

,CIfha§ yuqjk mßÈ tu iamrIlh;a BA f¾Ldj;a Èla lrkak

iv. PCB ;%sfldaKfha úfIaY cHdñ;sl ,CIhkhla ,shkak

4. f¾Ldjlska ndysr ,CIhl isg f¾Ldjlg ,ïNhla ks¾udKh 1. f¾Ldjla weo thg ndysrfhka P kï ,CIhla msysgqjkak

2. P ys ljlgqj ;nd f¾Ldj u; pdm folla ks¾udKh lrkak

3. tu pdm fol u; ljlgqj ;nd f¾Ldjg ndysrfhka fþokh jk f,i pdm folla ks¾udKh lrkak

4. tu fþok ,CIh yd P hd lrkak

5. wdk; f¾Ld follg iu ÿßka .uka lrk m:h tu f¾Ld fol w;r fldaKfha fldaK iuÉfþolhhs

1st. fldaKfha YS¾Ih u; ljlgqj ;nd ndyq fol u; l=vd È.lska pdm folla msysgqjkak

2nd. tu pdm fol u; ljlgqj ;nd fþokh jk f,i pdm folla wÈkak

3rd. YS¾Ih yd pdm fþok ,CIh hd lrkak


i. AB = 7 cm o C ̂B = 600 o A ̂C = 450 o jQ ABC ;%sfldaKh ks¾udKh lrkak

ii. tys BC mdofha È. uek ,shkak

iii. C ̂B fldaKfha iuÉfþolh ks¾udKh lrkak

iv. AB f¾Ldjg iudka;rj C yryd f¾Ldjla ks¾udKh lrkak th C ̂B

fldaKfha iuÉfþolh yuqjk ,CIh yuqjk ,CIh D f,i kï lrkak

v. ABDC p;=ri%hg j¾.M,fhka iudk jk yd AC mdohla jk

;%sfldaKhla ks¾udKh lr th ACE f,i kï lrkak


i. BC = 6 cm o A ̂C = 900 o BA = 4 cm jk ABC ;%sfldaKh ks¾udKh lrkak

ii. AC È. uek ,shkak

iii. by; AC ys È. weiqfrka √ ys w.h m<uq oYu ia:dkhg fidhkak

iv. ABC ;%sfldaKfha mßjD;a;h ks¾udKh lrkak

v. ;%sfldaKhl mßjD;a;fha flakaøh tu ;%sfldaKfha u mdohla u; msysgkafka ljr j¾.fha ;%sfldaK j,o @ fya;= olajkak

vi. uyd fldAKsl ;%sfldaKj, mßjD;a;fha flakaøh msysgkafka ;%sfldaKhg we;=,;skao msg;skao@

6. f¾Ldjlg iu ÿßka msysá m:h tu f¾Ldj fomiska .uka lrk iudka;r f¾Ld folls

1st. olajd we;s f¾Ldjl wdk; f¾Ldjla wÈkak

2nd. iEfok fldKh l=vd È.la iys;j weo .kak

3rd. f¾Ldfõ wfkla fl,jr weÈ fldaKh msysá me;a;g úreoaO me;af;ka ^taldka;r fldaK fuka& msgm;a lr .kak

4th. m<uqj weÈ fldaKfha È. ljlgqj wdOdrfhka ukskak

5th. tu ÿr fojk fldaKh u; msgm;a lrkak

6th. fojk fldaKh we§ug ljlgqj ;enQ ,CIh yd fojk fldaKh msgm;a lrk úg we;sjQ fþok ,CIh hd lrkak

7. fldaK ks¾udKh

1st. f¾Ldjla u; fldaKh ks¾udKhg wjYHh ,CIfha ljlgqfõ ;=v ;nd l=vd wrhlska hq;a jD;a; pdmhla ks¾udKh lrkak

2nd. lj lgqfõ ÿr fjkia fkdlr pdmfha uq,a fl,jr u; ljlgqj ;nd pdmfha fldgila fþokh lrkak

3rd. pdmh we§ug uq,a jQ ,CIh yd fþok ,CIh hd lrkak ks¾udKh ù we;af;a 600 ls

4th. tu fldaKh iuÉfþokh lrñka yd §¾> lrñka 15 ys .=Kdldr jk ´kEu fldaKhla ks¾udKh l< yelsh


i. 7 cm os. AB f¾Ld LKavh ks¾udKh lrkak

ii. B ̂P = 900 o AP = 4 cm o jk mßÈ P ,CIh msysgqjkak

iii. P yryd AB g iudka;r f¾Ldjla ks¾udKh lrkak

iv. P ̂B fldaKfha iuÉfþolh ks¾udKh lrkak tu iuÉfþolh;a P

yryd weÈ iudka;r f¾Ldj;a fþokh jk ,CIh C f,i kï lrkak

v. ABC ;%sfldaKh iïmQ¾K lr fldaKudkh Ndú;fhka A ̂C ys w.h uek ,shkak

vi. B ys C ,CIH yryd hkakd jQ AB mdoh u; flakaøh msysgkakd jQ jD;a;h ks¾udKh lrkak

vii. jD;a;fha flakaøh O hehs kï lr wrh uek ,shkak

600 300 450

1200 900 750

15. ndysr ,CIhl isg jD;a;hg weÈ iam¾Il

1st. jD;a;fha flakaøh yd ndysr ,CIh hd lrkak

2nd. iEfok f¾Ldfõ ,ïN iuÉfþolh ks¾udKh lrkak

3rd. ,ïN iuÉfþolh yd f¾Ldj yuqjk ,CIh flakaøh f,i o § weÈ jD;a;fha flakaøhg we;s ÿr wrh f,i f.k jD;a;hla ks¾udKh lrkak

4th. jD;a; fofla fþok ,CIhka ndysr ,CIfha isg hd lrkak

8. ;%sfldaK ks¾udKh

1st. fldaK § we;akï § we;s fldaKhla msysá ndyqjla m<uqj ks¾udKh l, hq;=h

o jD;a; pdm wdOdrhka b;sß mdo ks¾udKh l< yelsh

AB = 5 cm , BC = 4 cm , AC = 6 cm jk ;%sfldaKh

AB = 5 cm , A ̂C = 450 , B ̂C = 300 jk ;%sfldaKh

P AB = 5 cm , A ̂C = 600 , BC = 4 cm jk ;%sfldaKh

9. p;=ri% ks¾udKh

AB = 12 cm , B ̂D = 750 , AD = 7 cm jk p;=ri%fha DC f¾Ldj AB

f¾Ldjg iudka;r fõ DC = 7 cm jk ABCD p;=rih ks¾udKh lrkak

10. jD;a;hla u; mssysá ,CIhl§ jD;a;hlg iam¾Ilhla ks¾udKh

1st. flakaøh yd iam¾Ilh weÈh hq;= ,CIh hd lrk f¾Ldj Èla lrkak

2nd. iam¾Ilh weÈ ,CIfha§ weo we;s f¾Ldjg ,ïNlhla ks¾udKh lrkak

P

14. p;=ri%hlg j¾.M,hg iudk ;%sfldaKhla ks¾udKh

1st. § we;s p;=ri%fha úl¾Khla wÈkak

2nd. úl¾Kh fomi we;s tla YS¾Ihl§ úl¾Khg iudka;r f¾Ldjla ks¾udKh lrkak

3rd. tu iudka;r f¾Ldj yuqjk f,i Èla l< yels p;=ri%fha mdohla Èla lrkak

4th. tu f¾Ldj yd iudka;r f¾Ldj yuqjk ,CIhg úl¾Kfha tla fl<jrl isg f¾Ldjla weÈh yelsh th wÈkak

11. ;%sfldaKhl YS¾I iam¾I lrk jD;a;h tu ;%sfldaKfha mßjD;a;h hs

1st. § we;s ;%sfldaKfha mdo follg j;a mdo iuÉfþol ^,ïN iuÉfþol& ks¾udKh lrkak

2nd. tajd yuqjk ,CIh flakaøh f,io YS¾Ihlg we;s ÿr wrh f,io f.k jD;a;h ks¾udKh lrkak

A

B

C

D

12. ;%sfldaKhla ;=< msysá jD;a;h tu ;%sfldaKfha wka;¾ jD;a;h hs

1st. ;%sfldaKfha fldaK follgj;a fldaK iuÉfþol ks¾udKh lrkak

2nd. tajd yuqjk ,CIfha isg ;%sfldaKfha mdohlg ,ïNhla ks¾udKh lrkak

3rd. tu ,ïNh wrh f,i f.k jD;a;h ks¾udKh lrkak

13. ;%sfldaKhlg ndysßka msysá jD;a;h nys¾ jD;a;h hs

1st. ;%sfldaKfha mdo folla fomig Èla lrkak

2nd. iEfok ndysr fldaK j, iuÉfþol ks¾udKh lrkak

3rd. tajd yuqjk ,CIfha isg bÈßfhka we;s ;%sfldaKfha mdohg ,ïNhla ks¾udKh lrkak

4th. tu ,ïNfha È. wrh f,i f.k jD;a;h ks¾udKh lrkak

tharindu hasange. (bsc in computer engineering) dharmaraja … › pms › content › downlord ›...

Documents