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1 7 Shps 9 Unrstning lngth isovr n ojts Msurmnt n gomtry Wht informtion n w gthr from 2 shps n 3 ojts? E 7F 7G 7H 7I Tringl proprtis Quriltrl proprtis 2 shps n 3 ojts Isomtri rwings n plns Nts n prsptiv rwings Trnsltions, rottions n rfltions Unrstning ongrun Using ongrun iltions UNORRETE PGE PROOFS for ontinuing this unit, omplt th Prviw on pgs 00 0 of your Stunt Progrss ook.

2 4 7 Tringl proprtis isovr tringl is 2 (two imnsionl) shp with thr sis. onsir ths thr tringls (ignor th pink lins for th momnt). M m l L Tringls n nm, oring to thir sis, s quiltrl (ll sis qul), isosls (two sis qul) or sln (no sis qul). 1 Intify h tringl s ithr quiltrl, isosls or sln. Tringls n lso sri, oring to thir intrnl ngls, s ut-ngl (ll ut ngls), right-ngl (on right ngl) or otus-ngl (on otus ngl). 2 Intify h tringl s ithr ut-, right- or otus-ngl. 3 Hn nm h tringl in full. 4 Wht is th ngl sum of tringl? 5 Us protrtor to msur h ngl of ths tringls to prov your nswr to qustion 4. opy th tringls n mrk in ths ngls. Ths tringls hv h h on si tn n n trior ngl rwn in, shown in pink. Fous on th sln tringl. 6 How mny grs r thr in stright lin? 7 Wht is th siz of th ngl n? You shoul hv lry foun this in qustion 5. 8 Us your nswrs from qustions 6 n 7 to fin th siz th trior ngl, p. 9 togthr th ngls l n m. How os this totl rlt to th siz of ngl p? 10 Rpt th pross ov to fin th siz of th trior ngls for tringls n RST. 11 Fin th sum of th opposit intrior ngls for oth (ngls n ) n RST (ngls r n s). How o ths nswrs rlt to th siz of th trior ngls? 12 opy n omplt: Th siz of n ngl is qul to th sum of th two intrior ngls. 13 Us your unrstning of supplmntry ngls to plin why this works. mpl 1 think writ Fin th missing ngl in this tringl. n N p S R s r t T v mpl 2 think writ Fin th missing ngl for this tringl Th trior ngl of tringl is = qul to th sum of th two opposit = 150 intrior ngls. ths togthr. 2 Writ your nswr. Missing ngl is 150. ky is tringl is 2 shp with thr sis. Tringls n lssifi oring to thir si lngths (quiltrl, isosls or sln) or ngl siz (ut-ngl, right-ngl or otus-ngl). Th intrior ngls of tringl to 180. Th trior ngl of tringl is qul to th sum of th two opposit intrior ngls. now try ths 1 Nm ths tringls, onsiring oth thir sis n ngls. f 2 Fin th missing ngl in ths tringls Fin th missing ngl for ths tringls UNORRETE PGE PROOFS 1 Fin th sum of th two known ngls = Thr r 180 in tringl. Sutrt 145 from 180. = = Writ your nswr. Missing ngl is Tringl proprtis 5

3 6 plor 1 Origmi is th tritionl Jpns rt of foling ppr. On of th st known mols is th rn, pitur hr. Wht typs of tringls n you s in it? 2 Us your knowlg of th proprtis of tringl to fin th missing ngls in ths igrms. g g h h f i f 67 i 19 3 Invstigt th rltionship twn th iffrnt typs of tringls y looking t thir si lngths n ngls. n n quiltrl tringl hv right ngl? n n isosls tringl hv n otus ngl? You might lik to rt tl listing th si typs in olumns n th ngl typs in rows to show ths rltionships. 4 Us your knowlg of tringl proprtis n si lgr to fin th vlu of th pronumrls in ths tringls f R msurs th ngls in tringl n fins tht thy r in rtio of 1:2:3. Tht is, ngl is twi s ig s ngl n ngl is thr tims s ig s ngl. Fin th siz of h of th ngls in this tringl. lssify this tringl. Writ your own ril out tringl n giv it to lssmt to solv l ought this pnnt for nkl. Th shop ssistnt promis hr tht it ws n quiltrl tringl, ut whn l got hom sh wsn t sur. Us rulr n protrtor to fin if th shop ssistnt ws right, n stt wht typ of tringl it is. 7 Th Pnros tringl is fmous n impossil figur. Stt why it is impossil. lssmt ws givn numr of tringls to onstrut, ut is hving troul rwing thm. For h st of instrutions, rw igrm of th tringl or provi rson why it nnot rwn. i tringl with intrnl ngls of 90, 50 n 60 ii tringl with two intrnl ngls of 40 iii tringl with si lngths of 10 m, 3 m n 5 m iv right-ngl isosls tringl with two si lngths of 4 m n on of 5 m v tringl with two otus ngls sri th onitions you must follow whn you rw tringl. 8 W know tht th sum of th intrnl ngls of tringl is qul to 180, ut wht out th sum of th trior ngls? Follow ths stps to fin th sum of th trior ngls of tringl. rw thr iffrnt tringls (on sln, on isosls n on quiltrl). onsir th quiltrl tringl. i Mrk in ll intrnl ngls. ii Etn h si n mrk in h trior ngl. iii Fin th siz of h of th trior ngls n thm togthr. Wht o thy to? Rpt prt for your othr two tringls. Wht n you sy out th sum of th trior ngls of tringl? 9 W n us mths to onstrut quiltrl tringls, s shown hr. How mny mths wr us to onstrut ths thr quiltrl tringls? Us: i nin mths to onstrut four quiltrl tringls ii nin mths to onstrut fiv quiltrl tringls iii si mths to onstrut four quiltrl tringls. Us mths to onstrut h of th othr fiv tringl typs. rw ths in your ook, stting how mny mths you us for h si lngth. UNORRETE PGE PROOFS 10 rw thr tringls tht: hv t lst on ngl msuring 40 hv n otus ngl hv two qul sis. rflt How is knowlg of supplmntry ngls usful whn working with tringls? 7 Tringl proprtis 7

4 8 7 Quriltrl proprtis isovr quriltrl is 2 shp with four sis. 1 rw two intil opis of rnom quriltrl on pi of ppr n ut thm out. 2 ut on of th quriltrls in hlf so tht you mk two tringls. 3 How mny grs r thr in th ngl sum of tringl? 4 Us your nswr to qustion 3 to stt th ngl sum of quriltrl. 5 Rip th ornrs off th son opy of your quriltrl n pl thm togthr in wy tht provs your nswr to qustion 4. 6 Rpt qustions 1 5 with nothr quriltrl. Wht o you fin? Thr r si spil quriltrls, pitur low. E 7 opy this tl into your workook. 8 lssify shps F n Prlllogrm Rtngl Squr Rhomus Trpzium Kit omplt th first row. rwing of onsir th prlllogrm. shp 9 Look t h sttmnt in ll ngls th first olumn n i r qul whih ons pply to th ll sis r prlllogrm. Pl tik qul in ths lls. Opposit 10 ompr your nswrs to sis r lssmt s n isuss ny qul iffrns. Opposit 11 omplt th tl, fousing sis r on on shp t tim. prlll 12 Wht two onitions os On pir prlllogrm mt? of opposit 13 Wht othr shps lso sis r mt ths onitions? prlll Opposit 14 Us your nswrs to ngls r qustions 12 n 13 to qul plin why squr is typ of prlllogrm ut On pir of prlllogrm is not typ ngls r of squr. qul 15 Mk list of othr spil igonls rltionships tht you n mt t right s from th tl. ngls F mpl think writ lssify n fin th missing ngl in this quriltrl. ky is quriltrl is 2 shp with four sis. Som quriltrls hv spil proprtis involving sis n ngls. Ths r th prlllogrm, rtngl, squr, rhomus (lso known s imon), trpzium n kit. Quriltrls without spil proprtis r known s irrgulr quriltrls. Th ngls in quriltrl to 360. now try ths 1 lssify h of ths quriltrls. Giv rson for your nswr. 2 Fin th missing ngl in h of ths quriltrls lssify h quriltrl n fin th missing ngl Intify th quriltrl y onsiring Th quriltrl is its proprtis. Th quriltrl hs on trpzium. pir of prlll sis. 2 Fin th sum of th thr known ngls = ngls in quriltrl to 360. = Sutrt 225 from 360. = Writ your nswr. Th missing ngl is 135. UNORRETE PGE PROOFS Quriltrl proprtis 9

5 plor 1 Morn kits r rrly n tul kit shp. How mny iffrnt quriltrls n you s within this kit? opy h iffrnt quriltrl into your ook n nm thm. 2 Us your knowlg of quriltrls to: i nm h figur ii fin th missing ngls Ell mks numr of sttmnts out quriltrls. i if h sttmnt is tru or fls n rwrit ny fls sttmnts so tht thy r tru. squr is typ of prlllogrm. kit hs pir of prlll sis. prlllogrm is typ of rtngl. trpzium hs tly on pir of prlll sis. rhomus lwys hs four qul sis n four qul ngls. f rtngl lwys hs four qul sis n four qul ngls. 4 rt onpt mp showing th onntions twn ll th spil quriltrls. 5 Us your unrstning of quriltrl proprtis n si lgr to fin th vlu of th pronumrls in ths quriltrls f Whih quriltrls isply symmtry? rt tl showing h quriltrl with its lins of symmtry mrk. 7 trpzium os not hv to hv n is of symmtry. os this mn tht it nvr os? Eplin. 8 n irrgulr shp n on of two typs: onv or onv. onv shp hs intrnl ngls tht r ll smllr thn 180. onv shp hs t lst on rfl ngl (grtr thn 180 ). Eplin why onv quriltrl n hv only on intrnl rfl ngl. Fin th siz of th lrgst ngl if th othr thr ngls msur 20, 20 n 50. rw nothr two mpls of onv quriltrl. 9 In th isovr tsk you wr sk to ut quriltrl into two tringls. How os this prov tht th sum of intrnl ngls of quriltrl is 360? Kti rw two igonl lins n ivi rtngl into four tringls s shown. Sh si tht this mnt tht th ngl sum of rtngl is 720. Eplin why Kti s rsoning osn t work. (Hint: o th ngls t th ntr of th rtngl ount towrs th sum totl?) 10 Etrior ngls n foun for quriltrls s wll s tringls, s shown hr. rw rtngl n tn h si to mrk in th trior ngls. Wht is th siz of h trior ngl? Wht is th sum of th trior ngls? Rpt th tivity with nothr two quriltrls, t lst on of thm irrgulr. Wht n you sy out th sum of trior ngls for quriltrl? f Us your rsults from th prvious Eplor stion or rpt this tivity with tringl n stt th sum of th trior ngls of tringl. How os this ompr to your nswr to prt? 11 Eh sntn low givs lu out iffrnt quriltrl. Us th lus to o th following for h quriltrl: i fin th siz of h ngl ii rw th quriltrl iii nm th quriltrl. ll ngls r qul n ll sis r qul. Two ngls r qul ut hlf th siz of th othr two ngls. On ngl is twi th siz of nothr ut on thir th siz of th two lrgst ngls rw thr iffrnt: i squrs ii rhomuss iii rtngls iv prlllogrms. 11 isuss how you hv mor from in wht you rw in prts iii n iv ompr to prts i n ii UNORRETE PGE PROOFS f rw thr iffrnt: i kits ii trpziums. isuss how you hv mor from in wht you rw rflt How r th spil in prt ii ompr to prt i n qustion 12. quriltrls rlt? 7 Quriltrl proprtis

6 shps n 3 ojts isovr polygon is los 2 shp with stright sis. 1 Whih of ths figurs r polygons? 2 On of ths polygons is rgulr n on is irrgulr. Whih is whih? How o you know? 3 oth of ths polygons r pntgons. How mny sis o thy hv? 4 Look t th othr two figurs. How o thy rlt to th polygons? 5 On of ths 3 ojts is prism n th othr is pyrmi. Whih is whih? How o you know? 6 opy n omplt this tl. llow sp to show th nm n to rw on mpl of h shp or ojt. Nms for svn-si figurs hv n inlu for your rfrn. fiv sis si sis Nm Empl Nm Empl Polygon 3 ojt Rgulr Irrgulr Prism Pyrmi svn sis Nm rgulr hptgon irrgulr hptgon hptgonl prism hptgonl pyrmi Empl 7 rows to th tl so tht you n nm n rw shps n ojts with up to 10 sis. 8 Is irl polygon? Eplin. 9 row for irl to th tl n fill it in. 10 r thr othr shps or ojts tht hvn t n onsir? List n rw t lst thr othrs. mpl 1 think writ Nm this polygon. ll sis r not qul in lngth, so it is irrgulr. Thr r two rfl ngls, so it is onv. It hs ight sis, so it is n otgon. Th shp is n irrgulr, onv otgon. 1 2 mpl 2 think writ Nm this 3 ojt. ky is polygon is 2 shp with stright sis. Polygons n rgulr (ll sis n ngls th sm) or irrgulr. Irrgulr polygons n onv (ll intrnl ngls lss thn 180 ) or onv (t lst on rfl ngl). 3 ojts tht ontin only polygons r ll polyhr (singulr = polyhron). Mny polyhr n lssifi s ithr prisms (whih hv ns tht r mthing polygons) or pyrmis (whih hv on n finishing in point). ylinrs, ons n sphrs r mpls of 3 ojts tht r not polyhr. now try ths 1 Nm ths 2 shps. f 2 Nm ths 3 ojts. 1 i whthr th 3 ojt is prism or pyrmi. On n finishs in point, so it must pyrmi. 2 Look t th shp of th s. It is hptgon us it hs svn sis. 3 Nm it using hptgon n pyrmi. It is hptgonl pyrmi. f UNORRETE PGE PROOFS 7 2 shps n 3 ojts 13

7 plor 1 Nm ths shps n ojts. 2 In th prvious isovr tsk, w us tringls to vrify th ngl sum of quriltrl. W n o th sm for ny polygon. onsir this otgon. How mny sis os n otgon hv? How mny tringls is it split into? Wht is th iffrn twn ths two numrs? Us your knowlg of th intrnl ngl sum of tringl n your nswr to prt to lult th intrnl ngl sum for n otgon. os this work for ny otgon? rw two irrgulr otgons n fin thir intrnl ngl sum. f Why is it importnt tht th tringls ll strt from on vrt (ornr)? 3 Us th stps in qustion 2 to hlp you fin th intrnl ngl sum of: i pntgon ii hgon iii hptgon iv gon v ogon. Wht o you noti out th rltionship twn th numr of tringls in shp n th numr of sis th shp hs? 4 fmilir typ of onv polygon is th str. Nm h str oring to th numr of points it hs. Nm h str oring to propr mthmtil onvntions. Fin th intrnl ngl sum for h str. os it mth wht you foun in qustion 2? Wht os this mn for onv polygons? i ii iii 6 W n us our finings from qustions 2 n 3 to fin th siz of n iniviul ngl in ny rgulr polygon. How mny sis os hgon hv? Wht is th intrnl ngl sum of hgon? Us your nswrs to prts n to fin th siz of n iniviul ngl in rgulr hgon. Us th ov pross to fin th siz of n iniviul ngl in: i rgulr pntgon ii rgulr otgon iii rgulr gon. Why os this only work for rgulr polygons? 7 Us your finings from qustion 2 out th ngl sum in polygons to fin th missing ngl in h figur Us strws n lu-t to onstrut th 3 ojts foun in th Now try ths stion on pg Polyhr n m up of vrity of shps. ll polyhr hv flt fs, stright gs n vrtis. Look t th figurs shown. Wht is th iffrn twn th ttrhron n th trunt ttrhron? Is th trunt ttrhron polyhron? Eplin. opy th figur of th trunt ttrhron n pl ot on h vrt. How mny r thr? How os this ompr to th ttrhron? olour h g of th trunt ttrhron. How mny r thr? How os this ompr to th ttrhron? 10 Mny othr polyhr r otin y trunting (utting off vrtis of) ommon 3 ojts. rw n img of wht you woul pt ths ojts to look lik. trunt u trunt tringulr prism trunt squr-s pyrmi 11 3 ojt tht is not polyhron is torus, th mthmtil nm for th shp of onut. Wht othr ojts n you think of tht r in th shp of torus? 5 tsslltion is pttrn of shps tht hs no ovrlps or gps. Tsslltions n Eplin why torus is not polyhron. rgulr (ontining intil, rgulr polygons), smi-rgulr (ontining 12 Möius strip is n ojt with only on f n ny numr of rgulr polygons) or irrgulr (ontining ny shp). on g. 14 Wht typ of tsslltion is th on shown hr? Mk Möius strip y utting out thin strip of 15 rt tsslltion of your own, hoosing on or mor of th ppr n joining th ns togthr with hlf twist. shps shown in this tsslltion. Stt wht typ of tsslltion Tr your fingr ross th surf of th strip. Wht o you fin? you hv rt. Writ th lpht from th strt to th finish of th strip. rt nothr typ of tsslltion, hoosing whihvr shps Uno th strip n look t how th lpht is writtn on you lik. th strip of ppr. Wht o you fin? rflt How o w sri 2 Wht o you hv to think out whn rting tsslltions? Is Möius strip 2 or 3? Eplin your nswr. shps n 3 ojts? UNORRETE PGE PROOFS 7 2 shps n 3 ojts

8 16 7 Isomtri rwings n plns isovr ll of th 3 figurs in this ook r tully 2 rprsnttions of 3 ojts. It is importnt whn rwing 3 ojts tht th lins n sis r rwn orrtly to show thr imnsions. Isomtri ot ppr is usful tool whn rwing 3 ojts. onsir si rtngulr prism s shown in figur 1. It is 3 units long, 1 unit high n 1 unit wi. W n us isomtri ot ppr to hlp nsur tht w rw onsistnt n prlll lins. 1 How r lins of pth rprsnt using isomtri ot ppr? 2 Us isomtri ot ppr to rw rtngulr prism tht is: 3 units long, 2 units high n 1 unit wi 4 units long, 2 units high n 1 unit wi 4 units long, 2 units high n 3 units wi. 3 How o th figurs in qustion 2 iffr from figur 1? Figur 1 4 opy th rtngulr prism shown in figur 1 n lins to rprsnt it rokn up into us. 5 How mny us os this rtngulr prism ontin? Figurs 2, 3 n 4 hv n rt y ing mor us to th rtngulr prism. Figur 2 Figur 3 Figur 4 6 sri how thy iffr from th originl figur n from on nothr. (Hint: how mny tr us o thy hv n whr r ths pl?) Somtims, s figur gts mor ompl, it oms iffiult to urtly sri th shp, s prts of th ojt n om hin from viw. To minimis onfusion, w n rw st of plns for n ojt. st of plns lwys onsists of th front, right n top viw of n ojt, n th front must init with n rrow, lik in figur 5. front Figur 5 7 Look rfully t th viws, n. Whih mths th front viw of figur 5? 8 Stt whih of th rmining viws is th top viw n whih is th right viw of figur 5. 9 How os st of plns hlp us unrstn ompl 3 ojts? mpl think writ rw st of plns for this ojt. front ky is Isomtri ot ppr hs qully sp ots to hlp in rwing 3 ojts. Whn 3 ojts gt mor ompl it is usful to rw st of plns. st of plns onsists of front, si (usully right-hn si) n top viw. now try ths 1 rw ths ojts using isomtri ot ppr. u tll rtngulr prism hgonl prism tringulr prism 2 rw st of plns for h ojt. front 1 Look t th front of th ojt. From this ngl thr us r visil on th ottom n on on th top. rw this. 2 Look t th right si of th ojt. From this ngl four us r visil on th ottom n thr on th top. rw this. 3 Look t th top of th ojt. From this ngl four rows of us r visil: two us, thn thr us, thn two us, thn on u. rw this. UNORRETE PGE PROOFS front front front top right 7 Isomtri rwings n plns 17

9 plor 1 thing os r foun on mny hs in ustrli. rw st of plns for th lu thing o. Think rfully out wht shps you s for th front, right si n top viws. 2 W n us isomtri ot ppr to rw lttrs in 3. Wht lttr is shown hr? oul you rw this lttr nothr wy? Giv n mpl. rw ths lttrs using isomtri ot ppr. i L ii E iii O iv V v S 3 Us isomtri ot ppr to rw your own nm in 3. How tll n how wi is your rwing? 4 Plns oviously on t hv to only for ompl ojts m from us. rw st of plns for ths ojts. Think rfully out th shps tht you s from h viw. 5 Why is it hr to us isomtri ot ppr to rw pyrmis? 6 mol hous is shown. rw this on isomtri ot ppr. rw st of plns for th hous. rw wht you imgin lft si viw n k viw of th hous woul look lik. 7 Us isomtri ot ppr to rw th 3 ojt tht longs to h of ths sts of plns. 8 Mrio rw st of plns to mth this ojt, ut forgot whih ngl h rw it from. Rrw th ojt s Mrio sw it, llling th orrt si s th front. 9 Us isomtri ot ppr to sign n rw your own uiling. Inlu st of plns for it. 10 nothr strtgy to hlp rprsnt 3 ojts in 2 is to us shing. This u hs n sh in two iffrnt wys. Wht is iffrnt out th two sh us? opy th u n us shing to pit it in nothr two wys. 11 Us shing to pit th following ojts in t lst two iffrnt wys. 12 rw st of plns for: your hous shool uiling your fvourit stor th tllst uiling in your r th onstrution shown low. 18 front right top front right top 19 front right top UNORRETE PGE PROOFS front right top rflt front right top How r isomtri rwings n plns similr n how r thy iffrnt? 7 Isomtri rwings n plns

10 20 7E Nts n prsptiv rwings isovr Nts r grt wy to show 2 rprsnttions of 3 ojts, us you n fol thm up to rt th 3 ojts. onsir this rtngulr prism. 1 How mny fs os th rtngulr prism hv? 2 How mny iffrnt fs os it hv? 3 Of th thr nts shown hr, on os not work. Fin whih on n plin why. 4 Thr r mny iffrnt nts for this rtngulr prism. How mny n you fin? 5 rw nt tht is iffrnt from th ons on this pg n us it to onstrut th rtngulr prism. Inlu ts to mk it sir to onstrut. 6 Pl your onstrut prism on th sk n viw it t y lvl, ut on n ngl so tht it looks roughly lik figur E. o th lins of pth look prlll to you? Eplin. rwing n ojt from viw to show wht you tully s is ll prsptiv rwing. onsir ths four prsptiv rwings. To mk thm, vnishing point is rwn ov th front f of th prism n lins r rwn k to mt th vnishing point. E F G 7 Wht is th iffrn twn figurs n E? figurs E n F? 8 How os whr you hoos to pl th k gs of th prism fft th rwing? 9 How os th plmnt of th ot (th vnishing point) fft th rwing? mpl 1 think writ rw nt for this tringulr prism. 1 tringulr prism hs fiv fs, m up of four iffrnt kins. rw h iffrnt on. 2 rw th ottom f first n thn rrng th rmining fs in hopsoth styl nt. 1 2 mpl 2 think writ rt prsptiv rwing for th prism shown in Empl 1. ky is nt is 2 pln tht n fol to form 3 ojt. To rw nt it is sist to intify th ottom f of figur n pl th othr fs roun it in hopsoth rrngmnt. Prsptiv rwings rprsnt how ojts look in rl lif n mk us of vnishing point. For prsptiv rwing, lwys rw th front f first n nsur tht th k gs r rwn prlll to th front gs. now try ths For h figur, rw: nt prsptiv rwing. 1 rw th front f of th prism: in this s, tringl. 2 Pl vnishing point hin it somwhr n rw fint lins from h vrt towrs th vnishing point. 3 rw in th gs for th k of th prism. Mk sur thy r prlll to th front of th prism. 4 omplt th prism y mking th rmining gs soli n rsing th lft ovr fint lins n vnishing point UNORRETE PGE PROOFS E Nts n prsptiv rwings 21

11 plor 1 Nts n lso rwn for opn ojts. Th gift o to th right is tully m of two opn os on for th min o n on for th li. How mny fs os h prt of th gift o hv? rw nt for oth prts of th gift o. How o ths nts iffr? How is rwing nt for n opn ojt similr to rwing nt for pyrmi? 2 rw nt for n nvlop. You my wish to fin on to hlp you. 3 Thr r 11 uniqu nts for u. How mny n you fin? rful of rottions n mirror rfltions! 4 This is th nt us to rt sor ll. Whih two polygons mk up this nt? Wht shp r th ts? Whih polygons r usully olour lk n whih polygons r usully olour whit? Otin lrgr opy of th nt n olour in th pproprit polygons lk n th ts iffrnt olour. Us sissors n glu to ut out th nt n onstrut your own sor ll. 5 For ths nts: i intify whih ojt thy mk ii rw th ojt iii rt prsptiv rwing of th ojt. 6 Rrw h of th nts in qustion 5 s if thy wr opn ojts. 7 Mny popl hv iffiulty sing tht th nt in prt of qustion 5 longs to ylinr. Why o you think this is? Us pi of 4 ppr to monstrt how rtngl forms th min prt of ylinr. 8 Why is it hrr to rt prsptiv rwing for pyrmi? 9 For h of ths rwings: i intify th vnishing point ii rrw th ojt with iffrnt vnishing point. 10 onsir th uilings shown in this photogrph. How is th prsptiv shown iffrnt from th prsptiv rwings w v nountr so fr? rw opy of th uilings n intify th vnishing point for h. Whih uiling o you think is th tllst? How n you tll? 11 Us your unrstning of prsptiv rwings to writ your nm with vnishing point, lik in this mpl. Thn writ it son tim with iffrnt vnishing point. 12 This uiling is rwn in styl ll two-point prsptiv, rthr thn th singl-point prsptiv tht w hv n ling with so fr. Why is it ll this? How o you think th pross of rting two-point prsptiv iffrs from rting singl-point prsptiv? Intify th vnishing points in this rwing. rflt Whih rprsnttion Rrw th ojts from prts n of qustion 9 o you think is mor usful, nt or in two-point prsptiv. prsptiv rwing? Eplin. UNORRETE PGE PROOFS 7E Nts n prsptiv rwings

12 24 7F Trnsltions, rottions n rfl tions isovr Trnsltions, rottions n rfltions r ll trnsformtions. In this tsslltion, four shps hv n olour in. 1 Whih of th olour shps is vrtil rfltion of shp? 2 Whih of th olour shps is horizontl rfltion of shp? 3 Hs th rmining shp n rott or trnslt from shp? How o you know? 4 opy th tsslltion into your ook. 5 Fin ll th shps tht r trnsltions of shp n olour thm in r. 6 Fin ll th shps tht r trnsltions of shp n olour thm in grn. 7 omplt th tsslltion y olouring th trnsltions of shp (lu) n shp (yllow). Eh shp in th tsslltion n sri in numr of wys. Shp E, for mpl, n sri s: trnsltion of shp rottion thn trnsltion of shp rfltion thn trnsltion of shp rottion thn trnsltion of shp. 8 hoos shp in th tsslltion n sri it in minimum of four wys. 9 How r omintions of trnsformtions littl hrr to sri thn just on-stp trnsformtions? 10 rt your own tsslltion y using singl shp n sris of trnsformtions. E (Hint: it is st if th shp os not hv vrtil or horizontl symmtry. n you plin why this is?) mpl think writ Rott this shp 90 ntilokwis roun th point shown. 1 Slt vrt of th shp (pink ot). Sin th givn point of rottion (shown in lk) is on th shp, it is sir to hoos vrt tht hs n g (lso shown in lk) in ommon with it. Rott this g 90 ntilokwis roun th point of rottion. 2 rw in th rminr of th img. hk tht it is th sm shp ut rott. ky is n isomtri trnsformtion is on tht osn t hng th shp or siz of n ojt. Trnsltion, rottion n rfltion r ll isomtri trnsformtions. Trnsltion is whn shp or ojt is mov without turning or hnging siz. Rottion is whn shp or ojt is turn roun point. rfltion of shp or ojt is its t mirror img. Trnsformtions shoul lwys sri in s muh til s possil. Th trnsform shp is ll th img n shoul givn nm to rprsnt this, usully y ing sh to th originl nm, suh s. now try ths 1 Intify h of ths trnsformtions s ithr trnsltion, rottion or rfltion. 2 sri in full th trnsformtions prform on th shps in qustion 1. 3 Prform th following trnsformtions on this shp. Strt from th originl shp h tim. rflt in horizontl mirror lin trnslt 4 to th lft n 3 units up rflt in vrtil mirror lin rott 90 lokwis from th ottom right ornr trnslt 1 unit to th right n 2 units own f rott 90 ntilokwis from th ottom lft ornr UNORRETE PGE PROOFS 3 Ers th rrow n nm th finl img. 7F Trnsltions, rottions n rfl tions 25

13 plor 1 How woul you sri th trnsformtions shown in ths pinwhls? 2 rw shp of your hoosing onto grph ppr n ll its ottom lft ornr s (5, 5). Trnslt it oring to this squn of stps: i 4 right, 2 up ii 2 right, 3 own iii 3 lft, 4 up iv 1 lft, 6 own. Wht r th oorints of th ottom lft ornr of this finl img? 3 Olli n Sophi r plying gm similr to Pmn. Olli strts t (4, 2) n Sophi strts t (3, 8). Thy r h llow to tk fiv stps pr turn. Th ojt of th gm is to gt s los s you n to th othr plyr t th n of your turn. Howvr, if th othr plyr gts within on stp of you on thir turn, you los. Plot h roun of th gm for h prson using th movs list in this tl. Roun 1 Roun 2 Roun 3 Roun 4 Roun 5 Olli 2 right, 3 up 4 lft, 1 own 1 right, 4 up 3 right, 2 up 2 right, 3 own Sophi 1 right, 4 own 2 lft, 3 own 3 right, 2 up 4 right, 1 up 1 lft, 4 up Wht is th losst tht thy gt to on nothr? Who ws th winnr of this gm? Wht kin of trnsformtion os this involv? You might lik to tm up with lssmt n ply th gm yourslf. n you introu othr typs of trnsformtions into th ruls of th gm? 4 Whn you rott shp, th plmnt of th point of rottion is importnt in trmining th position of th img. Shp hs n rott in lokwis irtion from ll thr vrtis to prou thr iffrnt imgs. ll of th imgs hv n rott y th sm mount. How muh is this? sri how ths imgs iffr. How os hnging th position of th point of rottion fft th img? opy shp n pl point of rottion in its ntr. Rott shp roun this point of rottion 90 lokwis to prou fourth img. hoos nothr two points of rottion tht r not prt of th shp. Prou nothr two imgs y rotting th shp 90 lokwis roun ths two points. f How is this iffrnt from rotting roun point of rottion tht is on th shp? 6 Wht hppns if you rflt n img in two iffrnt mirrors? Lt s invstigt. Writ your nm (or ny wor you lik) n rw oth horizontl n vrtil mirror lin s shown in th igrm. Us ths mirrors to hlp you prou thr rfltions: on tht is rflt horizontlly, on tht is rflt vrtilly, n on tht is rflt oth horizontlly n vrtilly. Wht o you fin? o you noti nything out th rfltions? Now writ your nm (or th sm wor) n rw igonl mirror lin. Rflt in th igonl mirror lin. How os this ompr to th img tht is prou from oth horizontl n vrtil rfltion? mirror 7 How os th position of mirror lin fft th img? Lt s invstigt using th shp from qustion 4. opy th tringl n rflt it in h of th fiv mirror lins shown. Wht o you noti out th iffrn twn mirror lin tht is nt to th ojt s oppos to mirror lin tht uts through th ojt? Wht if you wr to onsir only on si of th mirror? Rflt through h mirror lin ut this tim only onsir wht is on th right of th mirror lin. How os this fft th img? Rpt prt ut only onsir wht is on th lft of th mirror lin. f How r th imgs prou in prt iffrnt from thos prou in prt? 8 Rpt th invstigtion from qustion 7, ut this tim rw your own horizontl mirror lins. Writ prgrph stting wht you fin n how it is iffrnt from th rsults you foun in qustion 7. 9 W n us th rtsin pln to hlp us urtly sri trnsformtions. rw rtsin pln tht hs sl from 0 to t lst 10 on oth th - n y-s. rw trpzium somwhr on th pln. (Hint: pl it somwhr nr th mil.) Ll th vrtis of th trpzium with oorints. Trnsform th trpzium oring to ths stps. Strt from th originl shp h tim. i trnslt 3 units to th right n 2 units up ii rflt in igonl mirror lin 26 5 Lt s onsir how hnging th istn of th point of rottion from th originl shp hngs th position iii rott 90 in n nti-lokwis irtion from th ottom right ornr of th img. Writ th oorints of h vrt of h trpzium from prt. 27 opy this shp n th fiv points of rottion shown. f Now trnsform th trpzium oring to th stps list, ut rthr thn strting from th originl shp Rott th originl shp 90 lokwis roun h h tim, ontinu on from h img rt. of th fiv points of rottion to form fiv imgs. g Writ th oorints of h vrt of th finl img sri th iffrn twn th imgs prou. in prt f. UNORRETE PGE PROOFS os th sm pttrn our for vrtil lin of points of rottion? opy th img n pl fiv points of rottion somwhr in vrtil lin. isuss your rsults. h How might writing th oorints of th vrtis hlp you whn intifying trnsformtions? rflt Wht ommon mistks o you think popl mk whn working with trnsformtions? 7F Trnsltions, rottions n rfl tions

14 28 7G Unrstning ongrun isovr 1 onsir ths two sugr glirs. How r thy iffrnt n how r thy th sm? 2 rw simpl figur (for mpl, tringl) n ut it out. 3 Prform ths trnsformtions on your figur n isuss how it hngs th siz n shp of your figur. Trnslt your figur up n to th right. Rflt your figur in horizontl mirror lin. Rott your figur 90 in lokwis irtion. ll ths trnsformtions r isomtri. n isomtri trnsformtion is on whih osn t hng th shp or siz of figur. If two figurs r intil in shp n siz, w sy tht thy r ongrunt. nt. 4 r th sugr glirs pitur ov ongrunt? How n you tll? 5 onsir ths two othr sugr glirs. How r thy iffrnt n how r thy th sm to th first two sugr glirs? 6 Eplin why nithr of ths two sugr glirs r ongrunt to th sugr glirs ov. mpl Intify ny pirs of ongrunt shps. think writ 1 Look t th shps to s if ny look th sm. 2 Shp E is thinnr thn ll th rst so it is not ongrunt to nything. 3 Shp is wir thn ll th rst so it is lso not ongrunt. 4 Shp is longr thn oth shps n so it is not ongrunt to nything. 5 Shps n look intil. Msur thm to hk. Shps n r ongrunt. E ky is Isomtri trnsformtions prou ongrunt figurs. ongrunt figurs r intil in shp n siz ut n in ny position or orinttion. Th symol for ongrun is. now try ths 1 i whthr h pir of shps is ongrunt. 2 Intify ny pirs of shps tht r ongrunt. UNORRETE PGE PROOFS N G L O M U P H V Q I W R X E J S K Y F T 7G Unrstning ongrun 29

15 plor 1 Whih of ths imgs of fish r ongrunt? E 2 Oftn whn shp hs n rott or rflt, w must mth orrsponing sis to hk if thy r ongrunt. For mpl, in th ongrunt figurs on th right, si mths si F. Mth th rmining sis for ths figurs. Mth th sis for th pirs of ongrunt figurs shown low. i L ii V iii Q R E F U K M F P G G T H W E F V U E I Y Z F W X 5 Ths pirs of figurs look ongrunt. Us rulr to msur thir sis n trmin if thy r ongrunt or not. 6 For ths pirs of figurs: i mth th orrsponing sis ii msur ll sis iii stt if th figurs r ongrunt. 7 For ths pirs of figurs: i trmin if thy r ongrunt ii plin your ision. 4 m 5 m 5 m 5 m 3 Eplin to lssmt th iffrn twn th mnings of th wor orrsponing whn you r tlking m out: 4.5 m 0.5 m 4 m i typ of ngl foun within prlll lins n trnsvrsl E ii ompring th sm ut F iffrnt sis or ngls in 8 Emily uys two pis of morn rt n hr frin ommnts tht shp. How o ths finitions G h pi is m up of ongrunt figurs. Emily isgrs. V rlt to h othr? trmin if h pi is m of ongrunt figurs. L K H I T 4 onsir ths shps. Provi rson for your ision. Tr or opy h shp n ut M S Provi rson 30 thm out, llling h with its J why you think 31 lttr. U somon might N Fin whih shps r ongrunt. R om to th wrong onlusion sri h pir of ongrunt Q O out this. shps s trnsformtion. For P Z Y Pi mpl, shp U is th rsult of X W trnsltion n rfltion in rflt How o w trmin if two horizontl mirror lin of shp. Pi fi gurs r ongrunt? m 1.5 m 5 m 6 m 6 m UNORRETE PGE PROOFS 3 m 1 m 7G Unrstning ongrun

16 32 7H Using ongrun isovr 1 Whih of ths four tringls r ongrunt? How o you know? 2 ll thr sis of th two ongrunt tringls r th sm lngth. o you think tht this is th s for ll ongrunt tringls? 3 rw tringl with si lngths of 4 m, 6 m n 7 m using pir of ompsss n/or protrtor. S pg 000 in Unit 6 if you r unrtin how to o this. 4 Now rw nothr tringl with ths sm si lngths, ut this tim strt th s with iffrnt si lngth. For mpl, if you us 6 m s th s, this tim us 4 m. 5 m 3.5 m 41 6 m m 7.5 m m 9 m 53 5 m 5 m 83 4 m m 6 m 5 ut out your son tringl n rott n/or flip it. os it fit tly on top of th first tringl you rw? Wht os this mn? Tringls tht hv ll thr pirs of sis qul in lngth r ongrunt n si to mt th onition SSS. 6 Why o you think it is nm SSS? Thr r othr onitions tht n us to trmin ongrun. SS is on of thm. 7 Wht o you think SS stns for? Orr is trmly importnt for ths onitions. In SS, th ngl must in twn th two sis. 8 Show tht only th pir of ongrunt tringls mt this onition. If th ngl is not twn th two sis, th sription oms SS. 9 Us tringls n to show tht if two tringls mt th onition SS it os not mn tht thy r ongrunt. 10 With lssmt, invstigt othr omintions of ngls n sis to s if you n fin othr onitions for ongrun. frin oing th invstigtion in qustion 10 i tht if ll thr orrsponing pirs of ngls wr qul () thn thos two tringls wr ongrunt. 11 Us tringls n to show tht this is not th s. nothr lssmt fins tht if two tringls hv pir of ngls n th si twn th ngls qul in siz (S) thn ths tringls r ongrunt. 12 opy tringl n mrk in th two ngls tht woul mk this onition tru if th si us ws 6 m. Your frin gts onfus n sys tht th rul osn t work us tringl hs two ngls (41 n 56 ) n si lngth (6 m) in ommon with tringl, ut thy r not ongrunt. 13 Eplin thir mistk. Why it is importnt tht th si lngth is twn th two ngls? 14 rt summry of th onitions tht init two tringls r ongrunt n onitions tht o not nssrily init ongrun. 15 Wht ommon mistks o you think popl might mk whn trying to trmin if two tringls r ongrunt? 56 mpl think writ i if this 1 Two sis n n ngl r givn tht r th sm Th two 8 m pir of in oth tringls. W must hk if this mts tringls r tringls is 82 onition for ongrun. not nssrily ongrunt, 6 m 2 In th first tringl th ngl is twn th two ongrunt s th giving sis, whih fits th SS onition for ongrun. only onition rson 6 m m 3 Th ngl in th son tringl is not twn thy mt (SS) for your th two sis, so it only mts th onition SS, is not onition nswr. for ongrun. 8 m whih is not onition for ongrun. ky is Two tringls r ongrunt if ll thir sis n ngls r qul. If pir of tringls mt th onitions shown in th tl, thy r ongrunt. Th spifitions (thr pirs of ngls qul in siz) n SS (two pirs of sis r qul in lngth n pir of non-inlu ngls r qul in siz) o not nssrily mn ongrun. now try ths SSS SS S Thr pirs of sis r qul in lngth. Two pirs of sis r qul in lngth n th pir of ngls in twn r qul in siz. Two pirs of ngls r qul in siz n th pir of sis in twn r qul in lngth. 1 i whih option (, or ) is ongrunt with th givn tringl. Giv rson. 4 m 4 m m 10 m 4 m 5 m 8 m 5 m m 6 m 2 i if ths pirs of tringls r ongrunt, giving rson for your nswr m m 10 m 9 m 11 m 11 m m 15 m 7 m 12 m m m m 3 m 13 m m 13 m m 54 UNORRETE PGE PROOFS 7H Using ongrun 33

17 34 plor 1 Elizth plys th tringl in hr shool n. Sh orrs nw tringl onlin ut thinks tht th on sh rivs is not th right on. Us your unrstning of ongrun to show tht ths two tringls nnot ongrunt vn if th imnsions of th photo mks th first tringl ppr iggr thn it is. 2 It is importnt to unrstn tht th spifitions SS n o not mn tht two tringls r not ongrunt, ut rthr tht it is not gurnt tht th tringls r ongrunt. In ft, if th spifition SS is ppli to right-ngl tringl it oms onition for ongrun ll RHS. Th longst si of right-ngl tringl is ll th hypotnus. Wht is th olour of th hypotnus in this tringl? If th R stns for right-ngl tringl, wht o you think th H n S stn for? Why must th hypotnus on of th sis for this onition? (Hint: if th right ngl is twn th two sis, wht onition os it om?) Knowing tht th tringl is right-ngl n inluing th hypotnus mns tht th thir si n lult using formul ll Pythgors Thorm (you will mt this nt yr). If you lult th lngth of th thir si, whih onition woul this now? (Hint: you woul know th lngths of ll th sis.) How os this show tht RHS is onition for ongrun? 3 Us th onition RHS to i if ths pirs of tringls r ongrunt. 3 m 13 m m 13 m 5 m 5 m 4 m m 4 Fin th missing si lngths or ngls in ths tringls, givn tht h pir is ongrunt. w 19 m 19 m 9 m f 17 m 62 7 m 80 y z 12 m v 107 k j 40 5 m m n l 40 7 m m 25 5 Stt th onition(s) tht you us to solv h prolm in qustion 4. 5 m 3 m 9 m 4 m h 22 m 22 m m g i j 6 nothr onition for ongrun is S. If w know two of th ngls in tringl, how o w fin th thir ngl? Using your nswr to prt, plin how w know tht two tringls tht hv two pirs of qul ngls must mt th spifition. S rfrs to two mthing pirs of ngls n on orrsponing pir of sis. Eplin why pir 1 mts th onition S ut pir 2 os not. n you plin how, if pir of tringls mt th onition S, thn thy lso mt th onition S? (Hint: you n to fin th thir ngl of th tringls.) rw pir of tringls to monstrt tht th spifition S is onition for ongrun. 7 For th pirs of tringls low: i i if thy r ongrunt, stting whih onition you us ii fin th vlu of th pronumrls if th pir is ongrunt. 6 m n 12 m q m 74 p 18 m m f 25 m 20 g r 48 m m 25 m m 9 m 35 Pir m m 10 m Pir 2 10 m 10 m m 70 y 25 z w m 5 m 12 m 70 8 Us ompss, rulr n/or protrtor to onstrut tringl with si lngths 3 m, 4 m n 5 m. onstrut ongrunt tringl y following th onition SS. Tht is, rw two si lngths with n ngl in twn tht mths th originl tringl. rw in th thir si lngth. os it mth th thir si in th originl tringl? o th ngl sizs mth s wll? Rpt prts n onstrut mor ongrunt tringls for th othr onitions for ongrun (S, SSS, RHS). Wht o you fin? 9 onsir th tringl with si lngths 3 m, 4 m n 5 m tht you rw in qustion 8. rw tringl oring to th spifition tht shows tht it os not mn ongrun. rw tringl oring to th spifition SS tht shows tht it os not mn ongrun. frin rw tringl oring to th spifition SS n foun tht it ws ongrunt to hr originl tringl. rflt Wht must you rmmr Eplin, using your nswr to prt, why this spifition is not onition for ongrun. whn using ongrun to solv prolms? UNORRETE PGE PROOFS 7H Using ongrun 35

18 36 7I iltions isovr Not ll trnsformtions prou intil figurs. iltion is on suh trnsformtion. onsir ths two figurs. 1 How r thy iffrnt to on nothr? How r thy similr? W woul sy tht figur is n nlrgmnt of figur. This rltionship n lso writtn th othr wy. 2 opy n omplt: Figur is rution of figur. Now onsir ths figurs. Figur is 1 m squr. 3 How woul you sri figur? 4 How muh iggr is figur thn figur? How muh iggr or smllr on figur is thn nothr is ll th sl ftor. W woul sy tht figur is n nlrgmnt with sl ftor of 2 with rspt to figur. 5 Stt th sl ftor for th following nlrgmnts with rspt to 1 m squr. 3 m squr 4 m squr 6 m squr 10 m squr 6 Stt th sl ftor for th following nlrgmnts with rspt to 2 m squr. 4 m squr 6 m squr 8 m squr 12 m squr 7 Nomi gv hr nswrs to qustion 6 s 4, 6, 8 n 12. Wht mistk i sh mk? Eplin whr sh wnt wrong n wht sh shoul hv on. t th strt of this tsk w sw tht iltion n sri s ithr n nlrgmnt from to or rution from to. 8 How o you think sl ftor might us to sri rution? Rmmr tht figur n sri s n nlrgmnt with sl ftor of 2 with rspt to figur. W n lso sy tht figur is rution with sl ftor of 1 2 with rspt to figur. 9 opy n omplt this tl. 10 sri th nlrgmnts in qustions 5 n 6 s rutions if th 1 m n 2 m squrs r th imgs rthr thn th originls. 11 Eplin in your own wors how sl ftor is us to sri iltions. iggr Smllr Two tims SF = 2 SF = 1 2 Thr tims SF = 3 SF = 1 3 Four tims SF = 1 4 Fiv tims Si tims Svn tims Eight tims Nin tims Tn tims mpl Shp hs n ilt n its img,, is shown. sri th iltion s n nlrgmnt or rution. Fin th sl ftor for th iltion. Hn sri th iltion in full. think ky is iltion is trnsformtion tht os not prou ongrunt figurs. iltions n ithr nlrgmnts (th img is iggr) or rutions (th img is smllr). iltions r sri using sl ftor, whr numrs ov 1 init n nlrgmnt n frtions twn 0 n 1 init rution. now try ths 1 sri ths iltions s ithr nlrgmnts or rutions. 2 For ths shps: i sri th iltion s n nlrgmnt or rution ii fin th sl ftor for th iltion 6 m 2 m 1 m 3 m 4 m 2 m 2 m 1 m iii hn sri th iltion in full. 33 mm 3 Us ths sl ftors to sri th possil iltions s ithr nlrgmnts or rutions m 4 Whih sl ftor in qustion 3 prous th grtst nlrgmnt? 9 m 3 m writ Th img ( ) is smllr thn th originl. This iltion is rution. To fin th sl ftor, w ompr orrsponing sis. Sl ftor = 1 3. Th originl msurs 3 m 9 m n th img msurs 1 m 3 m. Th img is thrfor thr tims smllr thn th originl. us it is rution, w writ this s frtion. Writ your nswr. This iltion is rution with sl ftor of 1 3. UNORRETE PGE PROOFS 11 mm 36 mm 12 mm 10 f m 7I iltions 37

19 38 plor 1 onsir this group of shps. Intify th originl n its img if: on is n nlrgmnt with sl ftor of 3 with rspt to th othr on is n nlrgmnt with sl ftor of 2 with rspt to th othr on is rution with sl ftor of 1 4 with rspt to th othr. 2 iltions n lso on in only horizontl 1 m irtion or only vrtil irtion. onsir ths figurs. Figur is iltion of figur. In wht 1 m 1 m 2 m 3 m irtion hs it n ilt? y wht sl ftor? Hs th horizontl lngth of figur hng with rspt to figur? Figur is lso iltion of figur. In wht irtion hs it n ilt? y wht sl ftor? Hs th vrtil lngth of figur hng with rspt to figur? With rspt to figur, rw n img tht hs n ilt y: i vrtil sl ftor of 3 ii horizontl sl ftor of 4 iii horizontl sl ftor of 6 iv vrtil sl ftor of 1 3 sri ths iltions: i s nlrgmnts or rutions ii y stting th sl ftor n th irtion of iltion. 3 m 3 m 5 m 2 m 4 m 3 m 3 m 2 m 2 m E 1 m E 1 m 2 m f 1 m 4 m 2. 2 m 2 m 3 m 2 m 6 m 4 m 2 m 2 m 4 m E 1 m 2 m 4 ilt this figur y: sl ftor of 2 vrtil sl ftor of 3 horizontl sl ftor of 4 vrtil sl ftor of 1 4 sl ftor of 1 3 f sl ftor of 1.5 g horizontl sl ftor of 1 2 h sl ftor of n img tht hngs only in siz (not in shp) ftr iltion is ll similr figur. Whih of th iltions from qustion 4 prou similr figurs? Knowlg of similr figurs n hlp us to solv prolms. onsir ths two tringls. Tringl is iltion with 35 sl ftor of 2 ompr to tringl. 3 m Wht os this mn? On si of tringl is 3 m in lngth. Wht is th lngth of th orrsponing si of tringl? On ngl in tringl is qul to 35. Wht is th siz of th orrsponing ngl in tringl? frin si tht us tringl is twi th siz of tringl tht th orrsponing ngl is 70. n you plin thir mistk? f opy n omplt ths sntns. For ny pir of similr figurs, to fin th si lngth of n img w th orrsponing si lngth of th originl figur y th sl ftor. Eh ngl is in siz to th orrsponing ngl in th originl figur. 6 For h pir of similr figurs: i us on pir of orrsponing sis to fin th sl ftor ii fin th missing si lngths n/or ngls for h pir. 12 m 6 m 2 m 3 m 33 m m 7 Is th smll og rution of th ig og? Eplin. UNORRETE PGE PROOFS z 4 m 24 m 4 m rflt 48 m 27 2 m 6 m Wht mistks o you think popl ommonly mk whn working with iltions? z 7I iltions 39

20 40 7 Shps n ojts rvis summris rt summry of th unit using th ky trms low. You my lik to writ prgrph, rt onpt mp or us thnology to prsnt your work. tringl quiltrl isosls sln ut-ngl right-ngl otus-ngl hoos 7 7 7E 7G trior ngl quriltrl polygon rgulr irrgulr onv onv 7 1 Th siz of ngl in this tringl is: Whih of ths sttmnts is tru? prlllogrm is squr. squr is rhomus. trpzium nnot hv right ngl. kit hs prlll sis. prism pyrmi polyhron f g vrt isomtri ot ppr 3 Whih of ths nts o not mk tringulr prism? 4 Whih trnsformtion os not prou ongrunt figurs? trnsltion rottion rfltion iltion 7H st of plns nts prsptiv rwing vnishing point isomtri trnsformtion trnsltion rfltion rottion ongrunt iltion nlrgmnt rution sl ftor similr figur 5 Whih rul oul you us to trmin if ths tringls wr ongrunt? nswr m 14 m 39 6 m m 11 m SS SSS S 1 Fin th missing ngls in ths tringls y Nm th tringls shown in qustion 1. 3 Fin th missing ngls in ths quriltrls w 122 n m 68 4 Nm th quriltrls shown in qustion p E 7F 5 Nm ths shps n ojts. 6 rw st of plns for ths ojts. 7 rw prsptiv rwing for h of th prisms in qustion 5. 8 onsir th shps shown on this gri. sri, n s trnsformtions of. Using s th originl shp h tim, rw imgs tht r: i rflt in igonl mirror lin ii rott 90 ntilokwis from th ottom right ornr iii trnslt 4 units right n 3 units up. Us ths figurs for qustions m 72 7 m 25 m f F m 15 m 72 E 22 m 21 m 41 7 m 7G 7H 7I 9 Intify ny pirs of ongrunt figurs. 10 Eplin your isions from qustion 9 with rfrn to on of th onitions for ongrun (SSS, SS, S, RHS) or onitions tht o not nssrily mn ongrun (, SS). 11 Tringl hs n ilt to prou nothr figur. Whih tringl is th img? Is it n nlrgmnt or rution? Wht is th iltion sl ftor? sri th iltion in full. nlys hoolt ompny is prouing nw prout n ns your hlp with th sign. Eh hoolt is n quiltrl tringl with si lngth 2 m n thy wnt to stk thm in prism, s shown in this front viw. In wht wys n you sri on tringl s trnsformtion of th othr? Wht shp is th front viw of th prism? rw this shp n ll it with its ngls n si lngths. Nm th prism of this shp. Us isomtri ot ppr to rw this prism. rw th following rprsnttions of this pkg. i nt ii prsptiv rwing iii st of plns Th ompny prous th of hoolts s shown m 2 m 2 m 2 m 2 m f Whih hoolt(s) n you rtin r th right imnsions? Eplin how you know. g Th ompny lso wnts to prou jumo siz in whih th imnsions r oul. Stt th sl ftor for this iltion n rw th nw hoolts n pkging, llling th ngls n si lngths. UNORRETE PGE PROOFS Shps Tringl n proprtis ojts 41

21 42 7 Shps n ojts onnt rm hom Wht woul your rm hom look lik? How woul you rrng th rooms? You n us th skills you hv lrnt in this unit to sign oth th insi n outsi of your rm hous. omplt th onnt stion on pgs of your Stunt Progrss ook to show ll your working n nswrs to this tsk. You will n to: i on th numr n typs of rooms in your hous i on th lyout of th hous (for mpl, will it hv lvls?) prou si st of plns for th intrnl lyout of th hous sign th outsi of th hous, inluing th roof prou st of plns for th hous prou til plns for t lst on room of th hous. sis roring ll working n nswrs to th tsk in your Stunt Progrss ook, you my lik to prsnt your finings s rport. Your rport oul in th form of: st of luprints n mol off-tl styl ook igitl prsnttion othr (hk with your thr). UNORRETE PGE PROOFS s itionl prprtion for th unit tst, omplt th Rviw on pgs 70 1 of th Stunt Progrss ook. 7 Shps n ojts 43