Pythagoras Theorem. Mathletics Instant Workbooks. Copyright

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1 Pythagoras Thorm Stunt ook - Sris I- y r Mathltis Instant Workooks opyright

2 Stunt ook - Sris I ontnts Topis Topi - Hypotnus o th right angl triangl Topi 2 - Naming th sis o a right angl triangl Topi - Slting th orrt Pythagoras rul Topi - Squars, squar roots an Pythagoran trias Topi - Fining th lngth o th hypotnus Topi - Fining th lngth o on o th othr sis Topi 7 - Misllanous qustions on Topi 8 - Prolm solving an Dat omplt Prati Tsts Topi - Topi tst Topi 2 - Topi tst uthor o Th Topis an Topi Tsts: S Kalra opyright P Larning

3 Topi : Hypotnus o th right angl triangl Qustion Nam th hypotnus o ah right angl triangl. a a P L q r N m n R Q p T W l J M R S U V K L Qustion 2 Nam th hypotnus o th triangl nam low in th iagram. a P Q L M E T J D S R K D PSR LJM T D N P S D E F H Q R PST D Qustion omplt th ollowing statmnts. FHG G a is th lngth o th si opposit to angl D. is th lngth o th si opposit to angl E. E F is th lngth o th si opposit to angl F. is th lngth o th hypotnus o ΔDEF. is th ara o th squar on th si opposit to D. D is th ara o th squar on th si opposit to F. opyright P Larning

4 Topi 2: Naming th sis o a right angl triangl For ah o th ollowing triangls, omplt th tal low an vriy that th squar on th hypotnus is qual to th sum o th squars on th othr two sis a a a opyright P Larning 2

5 Topi : Slting th orrt Pythagoras rul In th ollowing right angl triangls, irl th orrt statmnt. a a 2 = a s 2 = t 2 + u 2 2 = a S T t 2 = s 2 + u 2 2 = a u 2 = s 2 + t 2 D 2 a 2 = X Y a 2 = y 2 + z 2 2 = y 2 = 2 + z 2 2 = z 2 = 2 + y 2 U E F Z G H U a g 2 = h 2 + i 2 a u 2 = v 2 + w 2 h 2 = g 2 + i 2 v 2 = u 2 + w 2 i 2 = g 2 + h 2 w 2 = u 2 + v 2 V W I J a j 2 = k 2 + l 2 0 a 2 = k 2 = j 2 + l 2 2 = l 2 = j 2 + k 2 2 = K L D M a m 2 = n 2 + o 2 E a 2 = 2 + g 2 n 2 = m 2 + o 2 2 = 2 + g 2 o 2 = m 2 + n 2 g 2 = O N F G Q a p 2 = q 2 + r 2 2 a h 2 = i 2 + j 2 q 2 = p 2 + r 2 H i 2 = h 2 + j 2 P r 2 = p 2 + q 2 j 2 = i 2 + h 2 R I J opyright P Larning

6 Topi : Squars, squar roots an Pythagoran trias Qustion Us your alulator to in th ollowing squars. a 2 = 2 = 0 2 = 28 2 = 2 = 2 = g 0 2 = h 7 2 = i 8 2 = j 8 2 = k 2 = l 2 = Qustion 2 Us th squar root ky to in n. a n 2 = n 2 = 8 n 2 = 7 n 2 = 7 n 2 = 00 n 2 = g n 2 = h n 2 = i n 2 = 00 j n 2 = 280 k n 2 = 78 l n 2 = 2 Qustion Whih o th ollowing ar Pythagoran trias? a {2,, } {, 2, } {, 0, } {,, 0} {,, } {8,, 7} g {8, 0, 2} h {, 0, } i {, 8, 0} j {, 2, } k {,, } l {8,, 7} Qustion Prov that th ollowing triangls ar right angl triangls. a 2 opyright P Larning

7 Topi : Fining th lngth o th hypotnus Qustion Fin th lngth o th hypotnus in ah o th ollowing. (ll masurmnts ar in ntimtrs.) a Qustion 2 Fin th lngth o th hypotnus orrt to on imal pla. (ll masurmnts ar in ntimtrs.) a opyright P Larning

8 Topi : Fining th lngth o on o th othr sis Qustion In th ollowing triangls, in th lngth o th unknown sis. (ll masurmnts ar in ntimtrs.) a Qustion 2 Fin th lngth o th unknown si orrt to on imal pla. (ll masurmnts ar in ntimtrs.) a opyright P Larning

9 Topi 7: Misllanous qustions on Qustion In ah o th ollowing, n th lngth o th unknown sis (ll masurmnts ar in ntimtrs.) a y Qustion 2 Fin th lngth o th unknown si orrt to two imal plas. (ll masurmnts ar in ntimtrs.) a opyright P Larning 7

10 Topi 8: Prolm solving an Fin th lngth o th iagonal o a squar o si lngth m. 2 Fin th lngth o th iagonal o a rtangl o lngth m an with 2 m. What is th altitu o an quilatral triangl whos sis ar ah m long? Giv your answr orrt to two imal plas. mtr lar rsts against a wall an its oot is mtrs away rom th as o th wall. How high os it rah up th wall? Giv your answr orrt to two imal plas. Th sis o a rtangl ar 2 m an m. Fin th lngth o th iagonal. Giv your answr orrt to on imal pla. Th hypotnus o a right angl triangl is 0 m. I on o th shortr sis is 8 m, in th lngth o th othr si. 7 In a right angl triangl, th longst si is m an th shortst si is m. Fin th lngth o th thir si. 8 Fin th lngth o th unknown si in ah o th ollowing triangls, orrt to two imal plas. (ll masurmnts ar in ntimtrs.) a a 8 2 y Fin th primtr o th triangl low (orrt to on imal pla) y ining th hypotnus irst. 2 0 opyright P Larning 8

11 Topi Tst PRT Instrutions This part onsists o 2 multipl-hoi qustions Eah qustion is worth mark Fill in only ONE IRLE or ah qustion alulators ar NOT allow Tim allow: minuts Total marks = 2 Marks triangl is sai to satisy th rul 2 = a or whih spial triangl? aut angl right angl otus angl D 2 Th longst si o a right angl triangl is all th shortst si mil si hypotnus D Givn that 2 = a an a = 8, =, what is th valu o? D 2 an appli to aut angl triangls right angl triangls D otus angl triangls any triangl Th hypotnus o a right angl triangl is 7 m. I on si is m, th thir si is m 2 m 0 m D 8 m I two sis o a right angl triangl ar 2. m an m thn th hypotnus is 2. m 2. m. m D.8 m 7 Th Pythagoran rsult or a triangl right angl at is a2 = = a = a D 8 Th hypotnus o a right angl triangl is opposit to th aut angl right angl otus angl D I two shortr sis o a right angl triangl ar 7 m an 8 m, thn th hypotnus is 8 D 0 In a triangl right angl at, th hypotnus is nam as a D I two sis o a right angl triangl ar m an 8 m, thn th hypotnus is 0 m. m 2 m D 2 I n 2 = 20 thn n quals D 2 non o ths non o ths non o ths non o ths non o ths m opyright P Larning Total marks ahiv or PRT 2

12 Topi Tst Instrutions This part onsists o qustions Eah qustion is worth mark Writ answrs in th answrs-only olumn PRT Tim allow: 20 minuts Total marks = Qustions nswrs only Marks I n 2 = 8 thn in th valu o n Q 2 Is {, 8, 0} a Pythagoran tria? Prov that ΔPQR is a right angl triangl. P 27 R 2 Fin th lngth o th unknown si in th ollowing triangls orrt to two imal plas. 22 m m 7 m 7.2 m m. m m m m 7 m 2 m 0 2 m m 2 m m 8 m 2 m m 2 8 m m 7 m 20 m 2 m m opyright P Larning Total marks ahiv or PRT 0