ART LESSONS & EXERCISES

Transcription

1 RT LESSONS & EXERISES Rmón Gllego. English - Pge 1

2 English - Pge 2

3 STRTING UP WITH GEOMETRY. DEFINITION OF GEOMETRY Geometry is the rnch of mthem cs tht dels with the mesurements nd rel onships of lines, ngles, surfces nd solids. Geometry comes from Greek: geo = erth; metry = to mesure. So geometry mens to mesure the erth. LINE SEGMENTS. DDING SEGMENTS To dd segments we need to copy one segment er the other together on the sme line: H pencil for the solu on M N H 3H DEFINITION OF LINE SEGMENTS. line segment is prt of line tht is ounded y two endpoints. m The segment is prt of the line m. nd re the endpoints. P Q M N P + = MQ Q 3H pencil for everything ut the solu on The very first thing we mesure in geometry is line segment. LELLING IN GEOMETRY. In Geometry we lwys lel points with cpitl le ers nd lines with smll le ers. We cn lel segment using the cpitl le ers for the endpoints. Smll le ers re for lines, sides of polygon nd they cn lso e used to lel segments. We cn lso lel the segment MN s segment : SUTRTING SEGMENTS To sutrct segments we need to copy the shortest segment inside the longest, so the solu on is the rest. M N OPYING SEGMENTS. To copy segment we need to mesure the segment nd trnsfer tht mesurement to nother line. M N H pencil for the solu on H 3H P Q M P Q - = QN N 3H pencil for the rest of the exercise M N M N English - Pge 6

4 STRTING UP WITH GEOMETRY: LINE ND LINE SEGMENTS - PRTISE. 1. This is 3H line. Drw similr one on the right. 5. rete in the gp elow your own originl composi on, strct or figur ve, drwing with ruler line segments with different thicknesses. Use the pencils 3H nd H in order to get different line thicknesses. 2. This is n H line. Drw similr one on the right. 3. Here you re n H line er 3H line. Drw them equl gin on the right. 4. Here you re line segment in the line m. opy it gin in the right gp. Wtch the thickness of the lines. m 5. Here you re two segments nd D together, so D = + D. Drw it gin. D m 5. Lel the next segments. Rememer tht cpitl le ers re used for points. English - Pge 7

5 OPERTIONS WITH SEGMENTS 1 - PRTISE Exersice 1. Given the segments,, c nd d, do the oper ons indicted elow. M N Q c R O P S d T + + c O + d - d ( + ) - d English - Pge 8 TOTL TOTL TOTL TOTL TOTL oncept (0,6) Netness (0,1) Precision (0,1) Lels (0,1) H (0,1) oncept (0,6) Netness (0,1) Precision (0,1) Lels (0,1) H (0,1) oncept (0,6) Netness (0,1) Precision (0,1) Lels (0,1) H (0,1) oncept (0,6) Netness (0,1) Precision (0,1) Lels (0,1) H (0,1) oncept (0,6) Netness (0,1) Precision (0,1) Lels (0,1) H (0,1) TOTL MRK

6

7 OPERTIONS WITH SEGMENTS 2 - TIVITY Exersice 2.1. Given the segments,, c nd d, do the oper ons elow (5 points). M N Q c R SORING TIVITY Exercise 2.1. Drw n r s c composi on mde of segments (5 points). O P S d T + TOTL oncept (0,6) Netness (0,1) Precision (0,1) Lels (0,1) H (0,1) + c O TOTL oncept (0,6) Netness (0,1) Precision (0,1) Lels (0,1) H (0,1) + d TOTL oncept (0,6) Netness (0,1) Precision (0,1) Lels (0,1) H (0,1) - d TOTL oncept (0,6) Netness (0,1) Precision (0,1) Lels (0,1) H (0,1) ( + ) - d TOTL oncept (0,6) Netness (0,1) Precision (0,1) Group: Due dte: Lels (0,1) H (0,1) Project: Title: SEGMENTS Mrk: English - Pge 9

8 English - Pge 10

9 OPERTIONS WITH SEGMENTS 3 - EXTR TIVITY Exersice 3.1. Given the segments,, c nd d, do the oper ons elow. M N Q c R Exercise 3.2. The following drwing illustrtes the mesurements of uilding so the segments of the exercise 1 re the reference. Drw it elow with the segments of exercise 1 s mesurements to e trnsfered. Note: for this exercise you need to know how to trce perpendiculr lines with the set squres. O + P S d T TOTL oncept (0,6) Netness (0,1) Precision (0,1) Lels (0,1) d c d c - d c - d c - d d c + c O + d TOTL TOTL H (0,1) oncept (0,6) Netness (0,1) Precision (0,1) Lels (0,1) H (0,1) oncept (0,6) Netness (0,1) Precision (0,1) c P + TOTL d oncept (0,6) Netness (0,1) Precision (0,1) Lels (0,1) H (0,1) Lels (0,1) H (0,1) - d TOTL oncept (0,6) Netness (0,1) Precision (0,1) Lels (0,1) H (0,1) ( + ) - d TOTL oncept (0,6) Netness (0,1) Precision (0,1) Group: P Due dte: Lels (0,1) H (0,1) Project: Title: OPERTIONS WITH SEGMENTS Mrk: English - Pge 12

10

11 PRLLEL ND PERPENDIULR LINES WITH THE SET SQURES. THE SET SQURES OR TRINGLES The set squres or tringles re tools to drw geometry. They hve specific shpes with specific ngles so they llow us to drw prllel nd perpendiculr lines. There re two set squres: ) The 45 set squre, which is n isosceles right tringle (two equl sides, two ngles of 45 nd one right ngle) 45 hypotenuse (longest side) PRLLEL LINES Lines re prllel when they don t meet. You cn trce prllel lines with your set squres, following the next illustr on: The lines you get re prllel leg leg 3H ) The 60 set squre, which is sclene right tringle (different sides nd one right ngle). 60 hypotenuse (longest side) leg PERPENDIULR LINES Perpendiculr lines re lines which form n ngle of 90, tht is, right ngle. You cn trce perpendiculr lines with your set squres, following the next illustr on: leg 3H The lines you get re perpendiculr. The usul rrngement of the set squres is the following: 3H 3H We lwys set one leg of the 45 set squre ginst the hypotenuse of the 60 set squre nd we lwys drw lines with the hypotenuse of the 45 set squre. 90 You hve to turn the 45 set squre er drwing line. heck tht you lwys drw with the hypotenuse of the 45 set squre, nd you lwys set its legs ginst the hypotenuse of the 60 set squre, which remins st c English - Pge 14

12 PRLLEL ND PERPENDIULR LINES. EXERISES SET SQURES Write the mesurement in degrees for the corresponding ngles of the set squres. Test Recognise prllel nd perpendiculr lines nd choose the right nswer. Drwing prllel nd perpendiculr lines. omplete the next composi on following the p ern mde of prllel nd perpendiculr lines. Use the rulers. Exmple: ) Prllel lines. ) Perpendiiculr lines. ) Prllel lines. ) Perpendiiculr lines. ) Prllel lines. ) Perpendiiculr lines. ) Prllel lines. ) Perpendiiculr lines. hoose the right op on when working with the set squres. ) ) c) 3H 3H ) Prllel lines. ) Perpendiiculr lines. ) Prllel lines. ) Perpendiiculr lines. 3H English - Pge 15

13 SET SQURES, PRLLEL ND PERPENDIULR LINES - PRTISE 1 SET SQURES Write the mesurement in degrees for the corresponding ngles of the set squres. PRLLEL LINES Trce three prllel lines to the lines, c nd d. Wtch the exmple for line. PERPENDIULR LINES Trce three perpendiculr lines to the lines, c, nd d. Wtch the exmple for line. Exmple: c c hoose the right op on when working with the set squres. ) ) c) 3H d 3H d 3H English - Pge 16

14 SET SQURES, PRLLEL ND PERPENDIULR LINES - PRTISE 2. opy the p erns of prllel lines following the exmples nd instruc ons given. Horizontl prllel lines with ny direc on nd with ny sepr on you choose. Horizontl prllel lines with ny equl sepr on. Horizontl prllel lines with 4 mm of sepr on. Ver cl prllel lines with ny direc on nd with ny sepr on you choose. Ver cl prllel lines with ny equl sepr on. Ver cl prllel lines with 4 mm of sepr on. 3 mm Prllel lines with ny olique direc on nd with ny sepr on you choose. Prllel lines with ny olique direc on nd with equl sepr on you choose. Prllel lines with ny olique direc on nd with 3 mm of sepr on. You need perpendiculr line s reference for this sepr on. English - Pge 17

15 PRLLEL LINE TO NOTHER LINE THROUGH GIVEN POINT WITH THE SET SQURES. Drw prllel line to the line nd pssing through the point P. P lign the hypotenuse of the 45 set squre with the line. Put the hypotenuse of the 60 set squre ginst the leg of the 45 set squre. s the hypotenuse of the 45 set squre is not pssing through the point P, you hve to move this set squre un l it reches the point P. The 60 set squre must remin completely st c. The line s is the solu on. P P P H s DO IT Y YOURSELF. Trce prllel line to the given lines through the given points for ech cse. c P r W Q d M English - Pge 18

16 PERPENDIULR LINE TO NOTHER LINE THROUGH GIVEN POINT WITH THE SET SQURES. Drw perpendiculr line to the line nd pssing through the point P. P lign the hypotenuse of the 45 set squre with the line. Put the hypotenuse of the 60 set squre ginst the leg of the 45 set squre. Turn the 45 set squre, so its other leg is ligned with the hypotenuse of the 60 set squre. The 60 set squre must remin completely st c. heck tht the hypotenuse of the 60 set squre hs now perpendiculr direction to the given line. P P P 4 Move the 45 set squre so its hypotenuse psses through the point P nd trce the line s, which is the solu on. H DO IT Y YOURSELF. Trce perpendiculr line to given lines through the given points for ech cse. c s P P Q M English - Pge 19

17 PERPENDIULR LINE TO NOTHER LINE THROUGH N EXTERNL POINT WITHOUT THE SET SQURES. 1) One of the following pirs of lines re perpendiculr. hoose the right op on. ) ) c) 2) Wtch the steps to drw perpendiculr line to nother through n externl point just with the compss. Voculry. - segment isector. - segment. - drwing compss. - to trce. - rdius. - to join. - externl. - rc H H Q Q Q Q Q n n n n M N M N M N M N n The ini l situ on is tht you hve the line n nd the externl point Q. First f ll you need to trce n rc with centre Q nd with ny rdius, intersec ng the line n t the points M nd N. The next is trcing the segment isector of the segment MN. The segment isector of MN is the line s nd it must pss through the point Q. s s The line s is perpendiculr to n nd it psses through Q, so it is the solu on of the prolem. 3) Now do it y yourself. Trce the segment isector of the next segments. Q Q n n n n Q Q English - Pge 20

18 PERPENDIULR LINE TO NOTHER LINE THROUGH POINT ON THE LINE WITHOUT THE SET SQURES. FIRST METHOD. Wtch the steps to drw perpendiculr line to nother through point on the line, without using the set squres ut just with the compss nd ruler. Voculry. - segment isector or perpendiculr isector. - segment. - drwing compss. - to trce. - rdius. - to join. - rc H H Q Q Q n n n n n Q M Q N M Q N M N M N The ini l situ on is tht you hve the line n nd its point Q. First f ll you need to trce n rc with centre Q nd ny rdius intersec- ng the line n t the points M nd N. The next is to trce the segment isector of the segment MN. Tht is the reson segment isector is lso clled perpendiculr isector. s The segment isector of MN is the line s nd it must pss through the point Q. The line s is perpendiculr to n nd it psses through Q, so it is the solu on of the prolem. s 3) Now do it y yourself. Trce the segment isector of the next segments. Q n Q n t P i English - Pge 21

19 PERPENDIULR LINE TO NOTHER LINE THROUGH POINT ON THE LINE USING ONLY THE OMPSS. SEOND METHOD. Wtch the steps to drw perpendiculr line to nother through point on the line, without using the set squres ut just with the compss nd ruler. On this occsion perpendiculr isector hs not een used directly. Voculry. - segment isector or perpendiculr isector. - segment. - drwing compss. - to trce. - rdius. - to join. - rc s H H M P M M P Q n Q N n Q N n Q N n Q N n The ini l situ on is tht you hve the line n nd its point Q. First f ll you need to trce n rc with centre Q nd ny rdius intersec ng the line n t the point N. The next is to trce nother rc with centre N nd sme rdius intersec ng the previous rc t the point M. For the third step you need to trce nother rc with centre M nd sme rdius intersec ng the second rc t the point P. To finish the prolem, trce nother rc with centre Q nd sme rdius so you get the point H. Joining Q to H you get the line s, which is the solu on. 3) Now do it y yourself. Trce the segment isector of the next segments. Q n Q n t P i English - Pge 22

20

21 SORING TIVITY Drw perpendiculr line to the line m pssing through the point P. Use only the compss (2 points). oncept (0,12) Netness (0,2) Precision (0,2) Lels (0,2) H (0,2) TOTL Exercise: drw n r s c composi on mde of prllel nd perpendiculr lines. Use the set squres, so you cn drw fster (6 points). P m Drw perpendiculr line to the line n pssing through the point Q. Use only the compss. (2 points). oncept (0,12) Netness (0,2) Precision (0,2) Lels (0,2) H (0,2) TOTL Q n oncept (0,6) Netness (0,2) Precision (0,2) TOTL Group: Due dte: English - Pge 23 Project: Title: PERPENDIULR LINES WITH OMPSS Mrk:

22 English - Pge 24

23 NGLES. n ngle is the spce etween two intersec ng lines. The elements of the ngles re the vertex ( ver ces in plurl) nd the sides (the intersec ng lines). nd re the sides. is the vertex. α ngles cn e lelled with Greek le ers (α, β, γ, δ...) or with the symol ^ on the vertex lel: Â. 4. This is n stright ngle, which is equl to 180. Drw stright ngle on the right. 180 Drw n r s c composi on mde of mny different kinds of ngles. You cn use colours nd different thicknesses fro lines. 1. This is right ngle, which is equl to 90. You cn represent it with the symols or Drw two right ngles on the right like in the exmples. You should use your set squres. α α 2. This is n cute ngle, which is less thn 90. Drw n cute ngle on the right. β 3. This is n otuse ngle, which is greter thn 90. Drw n otuse ngle on the right. γ Group: Due dte: Project: Title: NGLES. Mrk: English - Pge 26

24 OPYING NGLES. opy the ngle α in the spce elow. Step 1: hoose ny point for vertex nd drw the side. Step 2: trce ny rc in the originl ngle α with ny rdius you choose nd drw it ging, with the sme rdius, in the copy elow. R 1 M Step 3: if you trnsfer the mesurement of the chord MN to the copy, you get the point M on the rc. R 1 M chord MN Do it y yourself. opy gin the ngle α. α α α N α N α Trnfer the mesurement of the chord MN R 1 R 1 M α N chord MN N H IMPORTNT VOULRY FOR THIS EXERISE Red the instruc ons nd underline these words. Try to find out their mening without dic onry. ngle rc vertex rdius mesurement point out go over You get the points M nd N in the originl ngle. However, you cn only drw the point N in the copy. You cn e sure tht M is going to e on the rc, ut where? If you find out where the point M is, you will e le to drw the side nd you would hve finished the prolem. Once you get the point M on the rc, you cn join the vertex to the point M, so you get the side. Don t forget to go over the sides nd with nd H pencil (the rest of lines re trced with 3H pencil) nd dd the rrows to point out the ngle α, which is the solu on. English - Pge 27

25 OPYING NGLES - PRTISE. Do it y yourself (Prc se) opy the followign ngles. c e g E ε α d β γ f D δ h i j English - Pge 28

26 DDING NGLES opying α dd the ngles α nd β. α V W β α R1 V Trce n rc with ny rdius R1 nd centre V in the originl ngle α. α R1 V Mesure the chord of the rc. W R1 β For β You need to trce the sme rc with the SME RDIUS R V V R1 V R1 α V β R1 α β α V R1 α + β opy α. Strt trcing line nd point for the ver ce. Trce n rc with the sme rdius R1. Trnsfer the mesure of the chord to the rc of α so you get. Join to V so you get the ngle α. Trnsfer the mesure of the chord for the rc of β so you get. Join to V so you get the ngle α. The solu on is the ngle mrked with very thick rc nd the rrows. Sides of the ngle re thick too. 3) Now do it y yourself. dd the next ngles. V α β W English - Pge 29

27 SUTRTING NGLES opying α Sutrc ng the ngles α nd β: the method is similr to the ddi on ut β must e copied inside α. V α W β α R1 V Trce n rc with ny rdius R1 nd centre V in the originl ngle α. α R1 V Mesure the chord of the rc. W R1 β For β You need to trce the sme rc with the SME RDIUS R V α R1 R1 R1 R1 V V V V opy α. Strt trcing line nd point for the ver ce. Trce the sme rc with rdius R1. Trnsfer the mesure of the chord to the rc of α so you get. Join to V so you get the ngle α. Trnsfer the mesure of the chord for the rc of β so you get. You hve to copy β inside α. The solu on is the ngle mrked with very thick rc nd the rrows. Sides of the ngle re thick too. 3) Now do it y yourself. Surtct the next ngles. V α β W English - Pge 30

28 NGLES. DDITION ND SUTRTION - PRTISE 1. Given the ngles elow, do the next exercises. 1) dd the ngles elow. α+β β+γ γ+δ α+δ α β γ 2) Sutrct the next ngles: α-β δ-β δ English - Pge 31

29 2. Do the next oper ons with the given ngles elow: (6 points): α β α +β α - β α + β - γ/2 3α/2 γ (α -β) x 2 (α + γ) / 2 NGLES. DDITION ND SUTRTION - PRTISE 2. English - Pge 32

30 OPYING FIGURES - PRTISE 3 opy nd lel the next figures (Lel ver ces, sides nd ngles). In order to copy these figures you need to pply wht you know out copying segments nd ngles. English - Pge 33

31 DRWING PORTRITS 1 (EXMPLE) When drwing protrit ngles etween key lines of the fce re very importnt for likeness. Wtch the next exmple nd complete it with colours nd detils. English - Pge 34

32 DRWING PORTRITS 2 (PRTISE 4) Drw the key lines on the fce elow, Roert Mitchum s fce. er drwing these key lines copy them in the ox on the right nd complete the portrit with detils nd colours. In order to copy these key lines you need to know how to copy segments nd ngles. English - Pge 35

33 DRWING PORTRITS 3 (PRTISE 5) Drw the key lines of on the fce elow, Grce Kelly s fce. er drwing these key lines copy them in the ox on the right nd complete the portrit with detils nd colours. In order to copy these key lines you need to know how to copy segments nd ngles. English - Pge 36

34 OPYING NGLES ND SEGMENTS (PRTISE 6) opy the top view of this strnge jet fighter, the YF-23. You will hve to mesure the ngles nd the segments with your compss nd trnsfer them to the right figure. You cn strt with the ini l ngle α nd the points nd. Once you hve completed the le side you will hve to pply symmetry to get the right side of the jet. olour it s you prefer when you hve finished copying the lines. α α D E F G G H I M K L J N English - Pge 37 K

35 opy this figure in the spce given on the right. You need to know how to copy ngles, how to drw equilterl tringles nd how to trnsfer mesures. The tools you need re only compss nd the set squres. Use the compss to trnsfer mesures. You cn colour it when you hve finished. Strt with the ngle Â. (PRTISE 7) English - Pge 38

36 LINE SEGMENT ISETOR OR PERPENDIULR ISETOR 1) One of the following figures is segment isector. hoose the right op on. Voculry. - ngle isector. - segment. - drwing compss. - to trce. - rdius. - to join. 2) Wtch the steps to drw segment isector H H The rdius must e the sme in oth steps M M M N N N You hve to trce the segment isector of the segment Trce n rc with centre nd rdius more thn the hlf of. This rdius is pproximte so you choose it. Trce nother rc with centre nd the sme rdius you used efore. You get the points M nd N. Drw line with 3H pencil joining M to N. The line of MN is the solu on of the prolem, so you must go over it with n H pencil. 3) Now do it y yourself. Trce the segment isector of the next segments. E F G H English - Pge 39

37 DO IT Y YOURSELF - PRTISE Trce the segment isectors of the next segments. H G E F D D English - Pge 40

38 IRUMFERENE PSSING THROUGH THREE POINTS To drw circumference pssing through three points you need to trce two segment isectors, like in the following method: Voculry. - circumference - through. - segment isector. - method. - to trce. - to meet. You re given three points: HOW TO DRW IRUMFERENE PSSING THROUGH THREE POINTS. METHOD STEP Y STEP. 1 This is the inform on you hve ini lly: just three points. 2 Drw the segments nd. 3 Trce the segment isector of, which is the line m. m You hve to drw the circumference which psses through them ll. Relize tht you need two segment isectors. oth segment isectors meet t O, the centre of the circumference we wnt to drw. 4 Trce the segment isector of, which is the line n. m n 5 The segment isectors m nd n meet t O, which is the centre of the circumference you hve to drw. m n Do it y yourself. ircumference pssing through, nd. O O O English - Pge 41

39 IRUMFERENE PSSING THROUGH THREE POINTS: FINDING THE ENTRE OF IRUMFERENE WHEN ITS POSITION IS NOT GIVEN. If you wnt to know where the centre of circumference is when this is not given, you cn use the method of the three points: just choose three points of the circumference nd trce the corresponding segment isectors. Find the centre of the following circumferences: English - Pge 42

40 DESIGN WITH IRUMFERENES. Wtch the following exmple nd drw your own design in the gp on the right. Group: Due dte: English - Pge 43 Project: Title: SEGMENT ISETOR ND IRUMFERENE Mrk:

41 Drw the perpendiculr isector of the next segment. (2 points). SORING TIVITY Drw n originl composi on with circumferences nd segment isectors, colouring the shpes they produce (6 points). omposi on mrk D oncept (0,12) Netness (0,2) Precision (0,2) Lels (0,2) H (0,2) TOTL Find the centre of the following circumference (2 points): oncept (0,12) Netness (0,2) Precision (0,2) Lels (0,2) H (0,2) TOTL Group: Due dte: English - Pge 45 Project: Title: SEGMENT ISETOR ND IRUMFERENE Mrk:

42 English - Pge 46

43 NGLE ISETOR 1) One of the following figures is ngle isector. hoose the right op on. ) ) m c) P M N n 2) Wtch the steps to drw n ngle isector m m m m m R M R M R M M β P α α α α α Q Q P P P P γ Q H N N N N n n n n n This is the ngle β. The ngle isector will divide it into two equl ngles. The first step consists of trcing n rc with ny rdius R, so it intersects the sides of the ngle t the points M nd N. For the second step, trce two rcs with centres t M nd N, nd sme rdius, so you get the point Q. Finlly, if you join the point P to the point Q, you get the line, which is the ngle isector. s is the solu on, you hve to drw it with H pencil. heck tht the ngle isector divides the ngle α into two equl ngles β=γ. 3) Now do it y yourself. Trce the ngle isector of the next ngles nd lel ll the points nd lines. α β γ English - Pge 48

44 DO IT Y YOURSELF - PRTISE Trce the ngle isectors of the next ngles nd choose the right sentence. E is less thn 90, so it is: ) n cute ngle. ) n otuse ngle. c) right ngle. is more thn 90, so it is: ) n cute ngle. ) n otuse ngle. c) right ngle. is less thn 90, so it is: ) n cute ngle. ) n otuse ngle. c) right ngle. G is less thn 90, so it is: ) n cute ngle. ) n otuse ngle. c) right ngle. H is equl to 90, so it is: ) n cute ngle. ) n otuse ngle. c) right ngle. O is equl to 180, so it is: ) stright ngle. ) n otuse ngle. c) right ngle. Question: how is the ngle isector of stright ngle? English - Pge 49

45 PERPENDIULR ISETOR ND NGLE ISETOR. EXERISES. Recognise the following drwings nd choose the right op on in ech cse. Go over the segment isectors with green colour pencil or felt- p pen. Go over the ngle isectors with red colour pencil or felt- p pen. olour the shpes produced y the segment isectors nd ngle isector. ) P M N m n ) ngle isector. ) Perpendiculr lines. c) Segment isector. ) ) ngle isector. ) Perpendiculr lines. c) Segment isector. c) ) ngle isector. ) Perpendiculr lines. c) Segment isector. English - Pge 50

46 H THE EQUILTERL TRINGLE n equilterl tringle is tringle with ll sides equl. Voculry. - Equilterl. - to lel. - pitl le ers. - Low cse le ers. - Ver ce. - Opposite. - Length. - vertex. - ver ces. c Lelling tringles pitl le ers for ver ces:,,. Low cse le ers for sides:,, c. Sme le er for ver ce nd its opposite sides:. Exercise: lel the next tringles nd mrk which one is equilterl. How to drw n equilterl tringle when given the side. side Do it y yourself. Drw n equilterl tringle using the folloging segment s side. 3H The rdius must e the sme in oth steps side 1 opy the segment of the side nd lel it. 2 Drw n rc with centre nd rdius the sme length of the given side. 3 Drw nother rc with centre nd the sme rdius: lenght of. oth rcs meet t the vertex. 4 Join to. Join to. is the equilterl tringle nd you cn trce it with n H pencil. English - Pge 51

47 DO IT Y YOURSELF - PRTISE Trce the equilterl tringles given the following sides. side side side English - Pge 52

48 THE SLENE TRINGLE (EL TRIÁNGULO ESLENO) sclene tringle is tringle which hs the sides ll different. Voculry. - circumference: circunferenci. - method: método. - to trce: trzr, diujr. - to meet: encontrrse. - rdius: rdio. You re given three segments for the sides of he tringle: c HOW TO DRW SLENE TRINGLE WHEN GIVEN THE SIDES. METHOD STEP Y STEP. 1 This is the inform on you hve ini lly: just three segments. 2 Drw one of the segments, for exmple the segment. Lel it keeping in mind the wy we lel tringles. 3 Trce n rc with centre nd rdius c. You hve to drw the sclene tringle which hs those segments s sides: c c c 3H c rdius = c c Rememering how to lel tringles. Lel the tringle ellow: 4 Trce n rc with centre nd rdius. 5 oth rcs meet t. Therefore you cn drw the sides nd. c c Do it y yourself. Drw the sclene tringle with sides, nd c. c rdius = c rdius = c H rdius = rdius = c English - Pge 53

49 DO IT Y YOURSELF - PRTISE Trce the sclene tringles given the following sides. c c English - Pge 54

50 THE RIGHT TRINGLE WHEN GIVEN OTH LEGS right tringle is tringle which hs n ngle of 90. Voculry. - right tringle. - right ngle. - leg. - hypotenuse.. - mesure. - to mesure. - to trnsfer. This right tringle: 90 c, : legs c: hypotenuse The sides which re perpendiculr re the legs: nd. The other side, the longest, is the hypotenuse (c). For this prolem you know only the legs, ut not the hypotnuse. So you will hve to fing out how to drw the tringle str ng just with the legs. HOW TO DRW RIGHT TRINGLE WHEN GIVEN THE LEGS. METHOD STEP Y STEP. 1 This is the inform on you hve ini lly: just the legs. 2 Drw one of the legs, for exmple the leg. Lel it keeping in mind the wy we lel tringles. 3 Drw perpendiculr line (m) to pssing through. 3H m 90 3H Rememering how to lel tringles. Lel the tringle ellow: 4 Mesure the length of nd trnsfer it to the line m, so you get the vertex. 5 Join to so you get the hypotenuse nd the right tringle. Do it y yourself. Drw the right tringle with legs nd. H Is this right tringle? m H m English - Pge 55

51 DO IT Y YOURSELF - PRTISE Trce the right tringles given the following legs. English - Pge 56

52

53 SORING TIVITY lssify the next ngles choosing the right op on. (1 point). 1 ) cute ngle. ) otuse ngle. c) right ngle. 2 ) cute ngle. ) stright ngle. c) otuse ngle. SORE (1 POINT) 1 (0,25) 2 (0,25) 3 (0,25) 4 (0,25) Drw n sclene tringle given its sides, nd c. Lel it properly. (3 points): c oncept (0,12) Netness (0,2) Precision (0,2) Lels (0,2) H (0,2) TOTL 3 4 TOTL ) stright ngle. ) otuse ngle. c) right ngle. ) cute ngle. ) stright ngle. c) right ngle. Drw n equilterl tringle given the side. Lel it properly. (3 points).t oncept (2) Netness (0,25) Precision (0,25) Lels (0,25) Drw right tringle given its legs. Lel it properly. (3 points). c oncept (0,12) Netness (0,2) Precision (0,2) Lels (0,2) H (0,25) H (0,2) TOTL TOTL Group: Due dte: English - Pge 57 Project: Title: TRINGLES Mrk:

54 English - Pge 58

55 TRINGLES OMPOSITION. Drw composi on mde of tringles. Use n 4 Gurro pper with ox similr to the one you cn see here. Group: Project: TRINGLES OMPOSITION Due dte: Mrk: 4 Gvrro pper. 130 g/m 2 Mrgins of 1 cm English - Pge 59

56 THE SQURE squre is polygon with four stright equl sides nd four ngles of 90. The lines which link its opposite ver ces (corners) re the digonls. They intersect t the centre of the squre. EXERISE Drw squre given the following side. d α β = = c = d α = β = γ = δ = 90 m O n m, n = digonls. m nd n re lso perpendiculr lines. O = centre of the squre. D δ c γ D D ridus = side ridus = side ridus = side The ini l inform on you hve is just the length of the side To strt, copy the side nd trce perpendiculr line through one of its endpoints. Tht is the line for side. The next is to trce n rc with rdius equl to the side, so you get the point on the side. You need the fourth ver ce, the point D. You know tht the distnce from to D must e the side. So you trce nd rc with centre nd rdius the side. The ver ce D must e on point of this rc. You lso know tht the distnce from to D must e the side, so you trce n rc with centre nd rdius the side. This rc intersects the other rc t the ver ce D. Joining the ver ces you get the squre D. English - Pge 60

57 SQURE OMPOSITION. Drw composi on mde of squres. Use n 4 Gurro pper with ox similr to the one you cn see here. Group: Project: SQURES OMPOSITION Due dte: Mrk: 4 Gvrro pper. 130 g/m 2 Mrgins of 1 cm English - Pge 61

58 English - Pge 63 GETTING OLOURS THROUGH POINTILLISM 1 Primry colours Mgent (1) Mgent(1) yn (1) Primry colours Yellow (1) Yellow (2) Yellow (2) Secondry colours Insted of mixing two primry colours, use directly the colour itself, if you hve the proper felt p. Red Red Ornge Yellow - Green ompre it with the colour produced y mixing primry colours Ornge Yellow - Green lck lck lck Grdients Red Ornge Yellow-green White White White yn (1) Yellow (1) Green Green lck Green White yn (2) Mgent (1) Violet Violet lck Violet White yn (1) Mixing complementry colours. yn (1) Mgent (2) Purple Purple lck Purple Ornge (2) Mgent (1) Green (1) Purple (1) Yellow (1) White