Know the sum of angles at a point, on a straight line and in a triangle


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1 2.1 ngle sums Know the sum of ngles t point, on stright line n in tringle Key wors ngle egree ngle sum n ngle is mesure of turn. ngles re usully mesure in egrees, or for short. ngles tht meet t point mke full turn so they up to 360. ngles tht meet t point on stright line mke hlf turn so they up to The three ngles of ny tringle up to 180. The ngle sum of tringle is 180. p r q p q r 180 Exmple lulte (o not mesure) the size of the ngles mrke with the letters, n. Give resons for your nswers. ) ) ) ) so is 120. ngles on stright line up to 180. ) so is 60. ngles t point up to 360. ) so is 70. The three ngles of tringle up to 180. Exerise 2.1 lulte (o not mesure) the size of the lettere ngles. Give resons for your nswers. ) ) ) Mths onnet 2G
2 lulte (o not mesure) the size of the lettere ngles. Give resons for your nswers. ) ) ) 25 p r q lulte (o not mesure) the size of the lettere ngles. Give resons for your nswers. ) g ) ) Use this igrm of ompss to lulte the following turns, ll in lokwise iretion: ) N to SE ) N to SW ) E to NW ) N to NW e) SE to NW f) NW to SE g) S to NE. Write own two turns tht re: h) 90 lokwise i) 45 lokwise j) 180 lokwise k) 135 lokwise. NW W SW N S 45 NE SE E Sketh these igrms n fill in the sizes of ll the mrke ngles. ) ) ) en is mking wooen puzzle. The igrm shows four of the wooen piees tht fit together long one of the eges Wht is the size of the re ngle? Use ruler n penil to rw lrge tringle with no sies or ngles the sme. Use ruler to fin n mrk the mipoint of eh sie. Use your ruler n penil to join the mipoints to mke nother tringle. Write own wht you notie out: ) the lengths of the sies of the two tringles ) the ngles of the two tringles. ngle sums 15
3 2.2 Nmes of ngles Distinguish etween n estimte the size of ute, otuse n reflex ngles Use protrtor to mesure ute, otuse n reflex ngles to the nerest egree Key wors ute right otuse reflex protrtor n ngle is mesure of turn n is usully mesure in egrees, or for short. n ute ngle is smller thn 90. right ngle is extly 90. n otuse ngle is etween 90 n 180. reflex ngle is greter thn 180 ut smller thn 360. We n use protrtor to mesure ngles The vertex is t the entre of the protrtor Sometimes it is neessry to exten the lines efore you n mesure n ngle. 180 The line segment is on the 0 line of the protrtor. Re off the size of the ngle from the orret sle. ngle 25 protrtor hs two sles: lokwise n n ntilokwise one. It is importnt to use the orret sle when mesuring ngles. Exmple ) Give the nme for this ngle. ) Mesure the ngle.? ) Reflex ) It is greter thn 180 ut smller thn 360.? The ngle is Exten the lines. Sine we know tht ngles t point up to 360, we n mesure the size of the ute ngle n then sutrt this from Mths onnet 2G
4 Exerise 2.2 rrnge these lettere ngles in orer of size, smllest first. e f g i) Give the nmes for eh of these ngles. ii) Estimte the sizes of eh of these ngles. ) ) ) ) e) f) Ply with prtner. Tke turns to rw n ngle. oth of you write own n estimte for the size of the ngle, then mesure it. Whoever is the loser to the estimte gins one point. If the estimte is within 5 of the tul size you get two points. Repet five times eh to fin the overll winner. Drw retngle with sies of 6 m n 10 m, using ruler n set squre. Drw in one of the igonls n mesure the ngles inite on this igrm. Write own wht you notie out: ) ngles n ) ngles n ) ngles n ) ngles n? 10 m 6 m Drw two stright lines tht ross like this: Mesure the size of the ngles on your igrm. Wht o you notie? Repet for nother set of stright lines tht ross. Wht o you notie? Drw ny tringle n exten eh of the sies s shown here. The outsie ngles re lle exterior ngles. ) Mesure eh of the six ngles inite, n mrk their sizes on the igrm. ) Do the ngles on eh stright line up to 180? ) together the ngles insie the tringle. Wht o they up to? ) Wht o the three she ngles outsie the tringle up to? e) Wht o you notie out the insie ngles? Wht o you notie out the outsie ngles? f) Repet prts ) to e) for nother tringle. Nmes of ngles 17
5 2.3 Mesuring n rwing ngles Mesure n rw lines to the nerest millimetre Mesure n rw ngles, inluing reflex ngles, to the nerest egree Key wors line segment ruler protrtor ute right otuse reflex line segment is line with fixe length n two enpoints. We n use ruler n protrtor to mesure n rw line segments n ngles urtely. efore rwing n ngle, you nee to think out wht it will look like. To help you rw it, first eie whether it is n ute ngle, right ngle, n otuse ngle or reflex ngle. For exmple, 153 is n otuse ngle. This mens tht it is more thn 90 ut less thn 180. It will look something like this: Exmple Drw line segment of length 3.4 m. Use protrtor to rw reflex ngle of 315 t the point. 1) 2) 3) 3.4 m 315 Drw line n mrk the point. Mesure 3.4 m from n mrk the point. Rememer to use shrp penil. To rw n ngle of 315 with n 180 protrtor, ple the protrtor so tht the 0 line is on so mrk n ngle of 45 using the sle tht goes lokwise. Tke the protrtor wy n join the mrk to the point. Mrk the ngle of 315. Exerise 2.3 Sketh, then rw the following ute ngles: ) 45 ) 63 ) 22 ) 85 Sketh, then rw the following otuse ngles: ) 165 ) 143 ) 102 ) Mths onnet 2G
6 Sketh, then rw the following reflex ngles: ) 310 ) 280 ) 220 ) 202 Drw line 5.6 m long with n ngle of 142 t one en. Drw line segment of length 6.4 m. Drw n ngle of 55 t with long line. Mesure 3.2 m long this line n mrk the point. 3.2 m m Here is sketh of wht your igrm shoul look like. Drw squre with sies of length 4.8 m, using set squre n ruler. Drw in igonl n mesure its length. 4.8 m 4.8 m ) ) Drw line segment of length 5.7 m. Drw n ngle of 43 t with long line. Mesure 7.3 m long this line n mrk the point. Join the point to the point to mke tringle. Mesure the thir sie of your tringle n the other ngles. 7.3 m m n you rw ifferent tringle with sies 5.7 m n 7.3 m n n ngle of 43? If so, mesure the length of the thir sie n the other ngles. ompre your tringles with prtner. Mesuring n rwing ngles 19
7 2.4 Drwing tringles 1 e le to rw tringles using ruler n protrtor Key wors rw sies ngles inlue ngle sketh vertex We n use ruler n protrtor to rw tringles urtely. To o this, we nee informtion out their sies n ngles. 2 m 3 m 50 This is lle the inlue ngle. If we know the lengths of two sies of the tringle n the size of the inlue ngle (the ngle in etween them), there is only one possile tringle tht we n rw. We ll this rwing tringle using SS (sie, ngle, sie) informtion. It is often helpful to rw sketh of the tringle, mrking on ll the informtion tht we know, efore we rw it urtely. Exmple Drw tringle with sies = 4 m n = 2.4 m where = 40. 1) 2) 4 m m 2.4 m 1) Drw sketh first n mrk on ll the mesurements. 2) Drw se line of 2.4 m. Mrk vertex for the ngle t. 3) 4) 40 4 m 3) Drw n ngle of 40 with long line. 4) Mrk point tht is 4 m wy from. omplete the tringle y joining. 2.4 m 2.4 m 20 Mths onnet 2G
8 Exerise 2.4 Drw the shpes skethe elow urtely. Mesure the ngle with the str in eh one n write it own. ) 5 m ) D ) G * * * 4 m 6 m 6 m 50 F E 6 m 120 I 5 m H ) Y e) Q f) 2 m * X m * 5 m Z T 5 m P * 4.5 m R S U 4 m Drw tringle with sies of length 5 m n 6 m, where the inlue ngle is 60. Rememer to rw sketh first. Mesure n write own the length of the thir sie. Drw tringle with sies of length 5.2 m n 6.4 m, where the inlue ngle is 48. Rememer to rw sketh first. Mesure the size of the other two ngles. up the three ngles. Is your nswer lose to 180? Drw tringle where 45 mm, 80 mm n 50. Mesure n write own the length of. Drw tringle DEF where DE 52 mm, EF 61 mm n DEF 160. Mesure n write own the length of DF. Mesure the size of the other two ngles. up the three ngles. Is your nswer lose to 180? is the ngle t. DEF is the ngle t E. Drw line segment of length 7.5 m. Drw n ngle of 74 t with long line. Drw n ngle of 50 t n exten the line until it meets the other line n mkes tringle. Mrk the point where the lines meet s. Mesure the sies n of your tringle n the ngle. n you rw ifferent tringle with sie of 7.5 m n ngles of 74 n 50? If so, mesure the length of the other two sies n the other ngle. ompre your tringles with prtner m 50 Drwing tringles 1 21
9 2.5 Prllel n perpeniulr lines Reognise n rw prllel n perpeniulr lines using ruler n set squre Reognise vertilly opposite ngles Key wors prllel perpeniulr right ngles vertilly opposite Prllel lines re stright lines tht never meet or ross. They re lwys the sme istne prt. We use rrows to show when lines re prllel. You n use set squre n ruler to rw prllel lines. Drw the line. Move the set squre long the ruler then rw the line D. D Perpeniulr lines ross or meet eh other t right ngles (90 ). You n use set squre n ruler to rw perpeniulr lines. Drw the line EF. Ple the set squre onto the line n rw perpeniulr line GH. E G H F Vertilly opposite ngles re equl. n re vertilly opposite ngles. n Exmple lulte the size of the lettere ngles. Give resons for your nswers euse vertilly opposite ngles re equl euse ngles on stright line up to euse vertilly opposite ngles re equl. You oul lso sy tht euse ngles on stright line up to 180. Exerise 2.5 Nme the pirs of lines tht re i) prllel ii) perpeniulr. ) ) ) ) e) f) g) h) i) 22 Mths onnet 2G
10 Whih is whih? opy these sentenes n fill in the gps. ) n re prllel. ) n re perpeniulr to eh other. ) is vertil. ) n re horizontl. There my e more thn one nswer. Drw these igrms urtely using ruler n set squre. E D F 5 m 5 m 10 m 6 m 10 m 5 m 5 m 12 m opy this igrm. olour eh pir of vertilly opposite ngles, using ifferent olour for eh pir. lulte (o not mesure) the lettere ngles. Give resons for your nswers. ) ) ) f e retngle mesures 6 m y 8 m. Use ruler n set squre to rw the retngle urtely n lel the prllel n perpeniulr lines. Mesure the lengths of the igonls. Tre this igrm. Mesure the lettere ngles (you my nee to exten the lines). hek tht ngles on stright line up to 180 n tht the ngles in the tringle up to 180. Wht o you notie out: j e ) ngles g n j ) ngles n f? g f Investigtion Here is piture of tngrm. These short lines men the line segments re the sme length. Use set squre n ruler to rw tngrm like this urtely. ut out the piees. Investigte shpes you n mke, whih hve: O ) t lest one pir of prllel sies ) t lest one right ngle. Mke s mny shpes s you n n rw them on plin pper. Prllel n perpeniulr lines 23
11 2.6 ngle lultions Know the sum of ngles in tringle Key wors vertilly opposite equilterl isoseles rightngle r p q 180 p q r 180 n ngles tht meet t The three ngles of Vertilly opposite point on stright line ny tringle up ngles re equl. up to 180. to 180. n equilterl tringle n isoseles tringle hs rightngle tringle hs three equl sies n two equl sies n hs one ngle of 90. three equl ngles. two equl ngles. Exmple 1 lulte the size of ngles, n. Give resons for your nswers euse it is vertilly opposite n ngle of euse the ngles of tringle up to euse the ngles on stright line up to 180. Exmple 2 lulte the size of. Give resons for eh step of your working. D 145? euse the ngles on stright line up to euse the se ngles of n isoseles tringle re equl euse the ngles of tringle up to Mths onnet 2G
12 Exerise 2.6 lulte the size of the lettere ngles. Give resons for your nswers g e f j 30 k l lulte the size of in eh of these igrms. Give resons for eh step of your working. ) ) ) lulte the size of the lettere ngles. Give resons for eh step of your working. ) ) e 165 Together, the pink tringle n the grey tringle mke one ig tringle. lulte the size of the ngles mrke, n. Write own the size of the ngles of the ig tringle, outline in lue. Wht o they up to? Sketh n isoseles tringle. Lel your igrm to show tht. Mrk 50. lulte the size of the other ngles in the tringle. ngle lultions 25
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