4 %w !capm &xjt&x!!n Fc/n*Are there times when you notice a relationship between the squares of the two legs of the triangle and the square of the hypotenuse? Drag the vertices of your triangle so that the relationship exists. Now look at the measures of angles A, B, and C. Is there anything special about the angles? Find a different triangle that satisfies the relationship with the squares of the legs and the hypotenuse. Take a look at the angle measures of this triangle. How do they compare to the measures of the angles of the previous triangle? Are you ready to make a conjecture about the squares of the legs and hypotenuse of the triangle and the measure of its angles? If so, test out your conjecture on some more triangles. If you're not ready, take a look at some more triangles and see if you can find a pattern.z39w!wn#:KThe measures of angles A, B, and C The value of a^2 + b^2 The value of c^2 P)4(Hrw!wnFgWhile you are changing the lengths of the sides of the triangle, keep your eye on the following things:Aw!wn"EUse the pointer tool to grab a vertex of the triangle and change the length of a side. For this exercise, you will want to keep side c as the longest side of the triangle.w!wn HH)q0@In this activity, you will explore the relationship between the measurements of the sides of a triangle and the measurements of its angles.(rtqHH'r ]H!nH0HM1)xHIMJ?1bThe square built on side a has area a x a = a^2. The square built on side b has area b x b = b^2. The square built on side c has area c x c = c^2. The sum of the areas of squares a and b = a^2 + b^2.HIP`MHIp@M(1HI MKINsnA Network Apps User TemAppleCD Audio PlayerAutomdCCZj`nCCCLkpnBCCH  nbCCZCCL?ᩎ<n naCCLCC?~  HN ncCCCCZ?kk  &@!nm9N0@R E4tNN@R`t+ m{!:A}ACB = dD$@$@ 0 0` Y` mTHH43 Ű Dj@0t `@|?D DB 4dY g4( 7D h )ǀ$ g$ 0 g\ ?!nm10ZSSWS`HHh| m{!:A}CAB = dD$@$@ 0 0` Y` mTHH43 Ű Dj@0t `@|?D DB 4dY g4( 7D h )ǀ$ g$ 0 g\ H!nm12^0R E4sz]^P0Rgv! m{!:A}CBA = dD$@$@ 0 0` Y` mTHH43 Ű Dj@0t `@|?D DB 4dY g4( 7D h )ǀ$ g$ 0 g\ J|nc1pCCCC vt vtCCLC.?5%F?5%FOfnc256ND*CCD CttCB CCZC ?5%F?5%F Brnc37`@pD CCC v vÅ@CCB?5%F?5%F . @`!nm10 E4b = A}CBA = dD$@$@ 0 0` Y` Length(Segment b) = *$p*$hDD D$@$@dň 4Pw_d ep ``D14:>THH43 Ű Dj@0t `@|?D DB 4dY g4( 7D h )ǀ$ g$ 0 g\  &_!nm3 E4pAbout Sketca = A}CBA = dD$@$@ 0 0` Y` Length(Segment a) = *$p*$hDD D$@$@dň 4Pw_d ep ``D14:>THH43 Ű Dj@0t `@|?D DB 4dY g4( 7D h )ǀ$ g$ 0 g\ D V^!nm4`0 P` c = A}CBA = dD$@$@ 0 0` Y` Length(Segment c) = *$p*$hDD D$@$@dň 4Pw_d ep ``D14:>THH43 Ű Dj@0t `@|?D DB 4dY g4( 7D h )ǀ$ g$ 0 g\ 'nmp ((p(CBDC? "'mnt(d00 CCCC? /(''naa( 0CҀC-CB? z!nm5  Calculator@ L  a{u:2} = = dD$@$@ 0 0` Y` Length(Segment a)^2 = *$p*$hDD D$@$@dň 4Pw_d ep ``D14:>THH43 Ű Dj@0t `@|?D DB 4dY g4( 7D h )ǀ$ g$ 0 g\!nm6 @ Calculatorgg Lg  b{u:2} = = dD$@$@ 0 0` Y` Length(Segment b)^2 = *$p*$hDD D$@$@dň 4Pw_d ep ``D14:>THH43 Ű Dj@0t `@|?D DB 4dY g4( 7D h )ǀ$ g$ 0 g\O!nm7  Calculatorgh Lg  c{u:2} = = dD$@$@ 0 0` Y` Length(Segment c)^2 = *$p*$hDD D$@$@dň 4Pw_d ep ``D14:>THH43 Ű Dj@0t `@|?D DB 4dY g4( 7D h )ǀ$ g$ 0 g\x}  nD I? K@DC af nF.nD Cv* F n/?<`DCB Y^ nHB$$??4"6.B`H`րCB qM!nm8\0S CalculatorIJ\S LI a{u:2} + b{u:2} = dD$@$@ 0 0` Y` 0(Length(Segment a)^2) + (Length(Segment b)^2) = DD D$@$@dň 4Pw_d ep ``D14:>THH43 Ű Dj@0t `@|?D DB 4dY g4( 7D h )ǀ$ g$ 0 g\|'nn2c1CCDC? 'noDCDC?}  nq(? b\ JH Db\\CCLDC?Z'nu(Cvc2?C@B|CGC? "'mnv.D.CvD7CvB$l?CCC_B?`N nx0JH Db\Ġ\JH\BxCCZCB?ܘ'&nab'(.Oc3*N*NB$DBC@Bx? /(''\nac\A :NDD*D D:DCBD@B~?X\ nae\gmD CvDCR**CCCB? 'anpCC@C~COG'RCCCC?!'\nwD.C3D@Lamx'CB CCMCB?$ ݝٜ''B'nadND*DBD@CD@  'Å@CCgDC0?'W\\nEDb\\0HCCCC@C  ;g'BwCC ) x}nG.D7DÀCA@! v'CCA *#16CvnI$?D!D%D C'ÅD C +&wV  nr%p? b\0JH Db\\DCCC?,H\ ns(CCCC v  v @CCCCZ?,f} nyJH Db]]0JH\?<CBCA?-w  nz JlCCCttBÆsCACC? -X6ps naf rmBsaBBCBCC BBBCBD C?.6Lh nagCLLmBsaBBD CD!D@CD CCCL?.