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S \ 6i _P  d X*  \ 6i _  i Z* H \ 0޽h ? 3380___PPT10.I!)0N0  %(  8 @`  @`  0DldD( ` ;1.3(2(  0pd@ SSegments and Their Measures 2 D(z     ,$D 0T  p`  #  p`"  0v:  0  0td"` P <GOAL 2`2  0p`   00yd 91 2    6}dp  JUse Segment Postulates 2z       ,$D 0T  p` #   `"  0v:  0  0Hd"` P <GOAL 2`2  0p`  0`d 92 2   6Td  a-Use the Distance Formula to measure distances. 2.  0d ,$0 oWhat you should learn> 2$D(D(z 0 6    ,$D 0  6d0 6 TTo solve real-life problems, such as finding distances along a diagonal city street.&U 2TfR  62$  O  Hd?"0@NNN?NP P ,$0 kWhy you should learn it8 2$D(H  0!޽h ? 33___PPT10.]R+6|D' d= @B D' = @BA?%,( < +O%,( < +D}' =%(D%' =%(D' =A@BB'BB0B%()?))D' =1:Bvisible*o3>+B#style.visibility<*%(DK' =+4 8?CB#ppt_h/20BCB#ppt_h/20BCB#ppt_hB*Y3>B ppt_h<*DK' =+4 8?CB#ppt_w+.3BCB#ppt_w+.3BCB#ppt_wB*Y3>B ppt_w<*DE' =+ 4 8?CB#ppt_x-.3BCB#ppt_xBCB#ppt_xB*Y3>B ppt_x<*D' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*D' =%(D' =%(D7' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-s6Bwipe(left)*<3<*D' =%(D' =%(D7' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-s6Bwipe(left)*<3<*D{ ' =%(D' =%(D' =A@BB'BB0B%()?D' =1:Bvisible*o3>+B#style.visibility<*%(DK' =+4 8?CB#ppt_h/20BCB#ppt_h/20BCB#ppt_hB*Y3>B ppt_h<*DK' =+4 8?CB#ppt_w+.3BCB#ppt_w+.3BCB#ppt_wB*Y3>B ppt_w<*DE' =+ 4 8?CB#ppt_x-.3BCB#ppt_xBCB#ppt_xB*Y3>B ppt_x<*D' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>B ppt_x<*D' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<*+p+0+0 ++0+0 +0N0   .DZ (  DF  ` D *  N  p` D  p``" D 0v:  0 D 0T+i"` P <GOAL 2`2 D 0p` D 0 91 2  D 0/ip LUSING SEGMENT POSTULATES 2F @` 'D @` (D 02iD( ` ;1.3(2( )D 0P&i@ SSegments and Their Measures 2 D( *D N:ijJ?"0@NNN?N  & ,$0 dIn geometry, rules that are accepted without proof are called or .f? 2&?& +D BxDi jJ?"6@ NNN?N ' ,$ 0 B postulates 2 " ,D BHi jJ?"6@ NNN?N ' ,$ 0 >axioms 2_ -D BLi jJ?"6@ NNN?N`  ,$ 0 {3Rules that are proved are called .,4 2!$ .D BXRi jJ?"6@ NNN?N`  ,$ 0 @theorems 2 H D 0!޽h ? 33ZR___PPT102.]R+ID'  = @B D' = @BA?%,( < +O%,( < +D' =%(D' =%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<**D%(D' =-o6Bdissolve*<3<**DD' =%(D' =%(DD' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*+D%(D' =-s6Bwipe(left)*<3<*+DD' =%(D' =%(DD' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*,D%(D' =-s6Bwipe(left)*<3<*,DD' =%(D' =%(DD' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*-D%(D' =-s6Bwipe(left)*<3<*-DD' =%(D' =%(DD' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*.D%(D' =-s6Bwipe(left)*<3<*.D++0+*D0 ++0++D0 ++0+,D0 ++0+-D0 ++0+.D0 +F  0N0 &  0'N P(     s *\hiS"  `  i  $ HX5d jJ?"6@ NNN?N@ ,$D0 RULER POSTULATE The points on a line can be matched one to one with the real numbers. The real number that corresponds to a point is the of the point.< 2zl  `  )   ,$D0W (  Bpi jJ?"6@ NNN?N `  The between points A and B, written as AB, is the absolute value of the difference between the coordinates of A and B. AB is also called the of AB. 2 E B %  BDjJ?"0@NNN?N& ' Blength 2l x   <  P ,$@0B ,  NDjJ?"0@NNN?Nx  2 .  NjJ?"6@ NNN?N@  2 0  NjJ?"6@ NNN?N @  l   @   ,$D0@   =  @    8    2  Ti jJ?"6@ NNN?Np  7A(2 3  Ti jJ?"6@ NNN?N p   7B(2 5  Ni jJ?"6@ NNN?N  Cnames of points(2B 6 B ZDjJ?"0@NNN?N p @ B 7  TDjJ?"0@NNN?N@ p  9  Ni jJ?"6@ NNN?N  Vcoordinates of points$ (2   :  N@i jJ?"6@ NNN?N 0  Fx1((2   ;  N̥i jJ?"6@ NNN?N  Fx2((2 B > TDjJ?"0@NNN?N0 B ? ZDjJ?"0@NNN?N z    F    ,$D 0 A  Ti jJ?"6@ NNN?N   AB = x2  x1 2B B  ZDo?"0@NNN?N  B C  ZDo?"0@NNN?N  B E TD>?"0@NNN?N ` ,$@0 @  G #  U ,$D 0N   0 H    0N   0 I    0n J  0"`> 0n2 K  0"` 00n2 L  0"` 0 M  08ik  A EXAMPLE 1 2 Z N  C *Aj0311784@ H  0޽h ? 33&&___PPT10%._`+D%' i= @B D$' = @BA?%,( < +O%,( < +D' =%(D' =%(D3' =4@BB BB%(D' =1:Bvisible*o3>+B#style.visibility<*$ %(D' =-o6Bdissolve*<3<*$ D' =%(D' =%(DD' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*' %(D' =-s6Bwipe(left)*<3<*' D>' =%(D' =%(D+' =4@BB BB%(D' =1:Bvisible*o3>+B#style.visibility<*< %(D' =-g6B fade*<3<*< D[' =4@BB BB%()))D' =1:Bvisible*o3>+B#style.visibility<*@ %(D' =-g6B fade*<3<*@ D' =%(D' =%(Dc' =4@BB BB%()))D' =1:Bvisible*o3>+B#style.visibility<*) %(D' =-o6Bdissolve*<3<*) D ' =%(D' =%(DD' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<** %(D' =-s6Bwipe(left)*<3<** D' =%(DI' =4@BB5BB%(D' =1:Bvisible*o3>+B#style.visibility<*E %(D' =+4 8?RCBBCB#ppt_wB*Y3>B ppt_w<*E D' =+4 8?RCBBCB#ppt_hB*Y3>B ppt_h<*E D' =-g6B fade*<3<*E DI' =4@BB5BB%(D' =1:Bvisible*o3>+B#style.visibility<*F %(D' =+4 8?RCBBCB#ppt_wB*Y3>B ppt_w<*F D' =+4 8?RCBBCB#ppt_hB*Y3>B ppt_h<*F D' =-g6B fade*<3<*F D' =%(D' =%(DD' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*+ %(D' =-s6Bwipe(left)*<3<*+ D' =%(Dz' =%(D"' =4@BB"BB%()))D' =1:Bvisible*o3>+B#style.visibility<*G %(D ' X=+4 . B(-#ppt_w/2)0B(#ppt_x)*Y3>B ppt_x<*G %(D' =+4 . B00B -1.0*[3>Bxshear<*G %(X))?)?D' =0l9 BBBBBB*<3<*G %(X))?)?D2' =+4 )B-(#ppt_h/3+#ppt_w*0.1)*Y3>B ppt_x<*G %(X))?)?++0+' 0 ++0+* 0 ++0++ 0 +i   0N0 kc`(  r  S i p  i   0i@ Q :Measure the green bar on page 17 (it has the word postulate in it) to the nearest millimeter. Then measure it again, this time placing your ruler with the 2 at one end of the bar. If you understand the Ruler Postulate, you ll get the same measurement as before. Your answer should beF 22 C8X/  Nio?"0@NNN?N5 U,$ 0 E about 133 mm. 2H  0޽h ? 33___PPT10f.` +(D'  = @B D' = @BA?%,( < +O%,( < +D' =%(D' =%(DD' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-s6Bwipe(left)*<3<*+8+0+0 +F  0N0 "x"P.O"(   " Ni jJ?"6@ NNN?N @ ,(2 @  ##  U,$D  0N   0 $   0N   0 %   0n & 0"`> 0n2 ' 0"` 00n2 ( 0"` 0 ) 0dik  A EXAMPLE 2 2 Z * C *Aj0311784@  + Bn jJ?"6@ NNN?N ,$@0 ^SEGMENT ADDITION POSTULATE If B is between A and C, then AB + BC = AC. Also, if AB + BC = AC, then B is between A and C. (Remember:  between implies the points are collinear.$ 2   :w8 @  4@ B ,  `Do?"0@NNN?Npp2 - TjJ?"6@ NNN?N@2 . TjJ?"6@ NNN?N @P 2 / TjJ?"6@ NNN?NP@ 0 N`n jJ?"6@ NNN?NpP  7A(2 2 N|n jJ?"6@ NNN?N` p  7B(2 3 NLn jJ?"6@ NNN?Np  7C(2l  p L p,$D 0B 8 NDjJ?"0@NNN?NB 9 NDjJ?"0@NNN?N  @  p H p@   =  5 N$n* jJ?"6@ NNN?N  <AB(2*B ;B ZD*jJ?"0@NNN?N B < ZD*jJ?"0@NNN?N  B F TD*>?"0@NNN?Np p2l  p M p,$D 0B : NDjJ?"0@NNN?N@  p I p@   @  6 N4*n jJ?"6@ NNN?N  <BC(2B >B ZDjJ?"0@NNN?N B ? ZDjJ?"0@NNN?NB G TD>?"0@NNN?N ppl p  N ,$D 0B AB NDjJ?"0@NNN?N  B B TDjJ?"0@NNN?N  @ p  Kp @ `   E`   7 N80n jJ?"6@ NNN?NP ` 0  <AC(2|B CB ZD|jJ?"0@NNN?N B D ZD|jJ?"0@NNN?N  B J TD|>?"0@NNN?Npp O N45n jJ?"6@ NNN?N  ,$0 tDo you see that the length of the blue and red segments added together is equal to the length of the purple segment?nu(2"*7| H  0޽h ? 33##___PPT10#.`@R+eDh#' An= @B D##' = @BA?%,( < +O%,( < +D ' =%(D' =%(DI' =4@BB5BB%(D' =1:Bvisible*o3>+B#style.visibility<*+G%(D' =+4 8?RCBBCB#ppt_wB*Y3>B ppt_w<*+GD' =+4 8?RCBBCB#ppt_hB*Y3>B ppt_h<*+GD' =-g6B fade*<3<*+GDI' =4@BB5BB%(D' =1:Bvisible*o3>+B#style.visibility<*+Gy%(D' =+4 8?RCBBCB#ppt_wB*Y3>B ppt_w<*+GyD' =+4 8?RCBBCB#ppt_hB*Y3>B ppt_h<*+GyD' =-g6B fade*<3<*+GyD' =%(DI' =4@BB5BB%(D' =1:Bvisible*o3>+B#style.visibility<*+y%(D' =+4 8?RCBBCB#ppt_wB*Y3>B ppt_w<*+yD' =+4 8?RCBBCB#ppt_hB*Y3>B ppt_h<*+yD' =-g6B fade*<3<*+yD ' =%(D' =%(D3' =4@BBB B%(D' =1:Bvisible*o3>+B#style.visibility<*L%(D' =-o6Bbox(out)*<3<*LD' =%(D3' =4@BBB B%(D' =1:Bvisible*o3>+B#style.visibility<*M%(D' =-o6Bbox(out)*<3<*MD' =%(D3' =4@BBB B%(D' =1:Bvisible*o3>+B#style.visibility<*N%(D' =-o6Bbox(out)*<3<*ND' =%( D' =A@BB5BB0B%()))D' =1:Bvisible*o3>+B#style.visibility<*O%(D' =+4 8?RCBBCB#ppt_wB*Y3>B ppt_w<*OD' =+4 8?RCBBCB#ppt_hB*Y3>B ppt_h<*OD' =-g6B fade*<3<*ODh' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*#%(D' =+4 8?RCBBCB#ppt_wB*Y3>B ppt_w<*#D' =+4 8?RCBBCB#ppt_hB*Y3>B ppt_h<*#D' =+K4 8?CBB#ppt_x+(cos(-2*pi*(1-$))*-#ppt_x-sin(-2*pi*(1-$))*(1-#ppt_y))*(1-$)CB?B*Y3>B ppt_x<*#D' =+K4 8?CBB#ppt_y+(sin(-2*pi*(1-$))*-#ppt_x+cos(-2*pi*(1-$))*(1-#ppt_y))*(1-$)CB?B*Y3>B ppt_y<*#+8+0+O0 + 0N0   p & (  X  S 0Aj01863440.pr  S Mn  n   NTNn jJ?"6@ NNN?N  Two friends leave their homes and walk in a straight line toward the other s home. When they meet one has walked 425 meters and the other has walked 267 meters. How far apart are their homes? Click for a hint., 2R  C *Aj01957346PSpR  C *Aj02293530P lR  C *Aj02167920@pB  ZD|Ԕ?"0@NNN?Npp,$@ 0B  @  `DԔ?"0@NNN?Np0p,$@ 01 " NWn jJ?"6@ NNN?Npp ,$ 0 A425 m 267 m 2d # NHAd jJ?"6@ NNN?N PP ,$ 0 t(The solution is 425 m + 267 m = 692 m. 0) 2 * & B\no?"0@NNN?N @@ ,$0 ;Answer: 2H  0޽h ? 33~v___PPT10V.`@+,OD' fn= @B D=' = @BA?%,( < +O%,( < +Dx' =%(D ' =%(D/' =4@BB#BB%()?)?D' =.K7 BBBBB]M -2.5E-6 -2.36994E-6 L -0.23281 -2.36994E-6 *3>*B ppt_xB ppt_y=@0BBAApBBB<*D+' =4@BB?BB%()?)?D' =.G7 BBBBBYM -1.38889E-6 3.98844E-6 L 0.51372 -0.0007 *3>*B ppt_xB ppt_y=@0BBAApBBww>Br<*D9' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =-u6Bwipe(right)*<3<* D7' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-s6Bwipe(left)*<3<*D>' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*"%(D'  =-m6Bbox(in)*<3<*"D' =%( D@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*&%(D' =-o6Bdissolve*<3<*&D' =%(D' =%(DD' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*#%(D' =-s6Bwipe(left)*<3<*#++0+"0 ++0+#0 ++0+&0 +3 0N0   ( (  (r ( S ,xn   n ) 8     (  3 ( Nyn jJ?"6@ NNN?N  D<4___PPT9 #Measure the length of BC at the top of page 18 to the nearest millimeter. A car with a trailer has a total length of 27 feet. If the trailer has a total length of 13 feet, how long is the car?. 28X (  0e0e    BCDEF AjJ 8c8c     ?1 d0u0@Ty2 NP'p<'pA)BCD|E||@ "0e@     @ABC DEEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abN E5%  N E5%  N F   5%    !"?N@ABC DEFFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `ab @ AU ( Nn jJ?"6@ NNN?N ,$ 0 e 2. 14 ft* 28XE ( Nn jJ?"6@ NNN?N,$ 0 U1. about 25 mm* 2H ( 0޽h ? 33___PPT10.``+[D'  = @B D' = @BA?%,( < +O%,( < +D' =%(D' =%(DD' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*(%(D' =-s6Bwipe(left)*<3<*(D' =%(D' =%(DD' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*(%(D' =-s6Bwipe(left)*<3<*(+p+0+(0 ++0+(0 +D0N0    0(  0F  ` 0  `T  p` 0#  p``" 0 0v:  0  0 0n"` P <GOAL 2`2  0 0p`  0 0(n 92 2   0 6Ԯnp NUSING THE DISTANCE FORMULA 2F @`  0 @` 0 04nD( ` ;1.3(2( 0 0n@ SSegments and Their Measures 2 D( 0 N7d jJ?"6@ NNN?Np v ,$0 kTo find the distance between two points in a coordinate plane, we use the .Bl 2- 8 0 Nn jJ?"6@ NNN?NW w ,$ 0 HDistance Formula 2H 0 0!޽h ? 33___PPT10.]R+iߑD'  = @B D' = @BA?%,( < +O%,( < +D' =%(D' =%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*0%(D' =-o6Bdissolve*<3<*0D' =%(D' =%(DD' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*0%(D' =-s6Bwipe(left)*<3<*0+p+0+00 ++0+00 +Q0N0 [S.40 (  4 @  4#  +,$D0N   0 4   0N   0  4   0n  4 0"`> 0n2  4 0"` 00n2  4 0"` 0  4 0nk  A EXAMPLE 3 2 Z 4 C *Aj0311784@  4 N|njJ?"6@ NNN?N  LTHE DISTANCE FORMULA 2k 4 N n jJ?"6@ NNN?N@  cIf A(x1, y1) and B(x2, y2) are points in a coordinate plane, then the distance between A and B is 0c 2(2****> 40 c $0e0eA     ? A@  AjJ 8c8c     ?1 d0u0@Ty2 NP'p<'pA)BCD|E||s " 0e@        @ABC DEEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abN E5%  N E5%  N F   5%    !"?N@ABC DEFFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abH $D0 n$ 8 `0  .40`  4 Nn jJ?"6@ NNN?N`0PP 7y(2 4 N0n jJ?"6@ NNN?N   7x(2B 4  fDjJ?"0@NNN?N` B 4  fDjJ?"0@NNN?N @ B 4 TDo?"0@NNN?N@ e 4 TlKd jJ?"6@ NNN?N   A(x1, y1)v 2**e !4 T8t jJ?"6@ NNN?Np  B(x2, y2)v 2**2 "4 TjJ?"6@ NNN?Nu  2 #4 TjJ?"6@ NNN?N(X '4 N tjJ?"6@ NNN?NP ` <,$D 0 OImportant!!! Pay close attention to where the coordinates fit in the formula!.P(2AB (4  `D*Ԕ?"0@NNN?N `,$D 0B )4  `DԔ?"0@NNN?NP ,$D 0B +4@  `D*Ԕ?"0@NNN?NP@ ,$D 0B ,4@  `DԔ?"0@NNN?N@p ,$D  0H 4 0޽h ? 3311___PPT101.aQ0+dDK1' = @B D1' = @BA?%,( < +O%,( < +DU' =%(D' =%(D' =4@BB3BB%(D' =1:Bvisible*o3>+B#style.visibility<*4%(D' =-g6B fade*<3<*4)?D' =0l9 BB A AHCC*<3<*4)?D' =0l9 BBHCCBB*<3<*4%()?D' =1:B (0.5)*Y3>B ppt_x<*4D ' =+4 . B (0.5)0B(#ppt_x)*Y3>B ppt_x<*4%()?D' =1:B(#ppt_y+0.4)*Y3>B ppt_y<*4D' =+4 . B(#ppt_y+0.4)0B(#ppt_y)*Y3>B ppt_y<*4%()?D"' =%(D+' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*'4%(D' =+4 8?dCB1+#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*'4D' =+4 8?dCB0-#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<*'4D' =%(D9' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*(4%(D' =-u6Bwipe(right)*<3<*(4D' =%(D)' =4@BB BB%(D' =-g6B fade*<3<*(4D' =1:Bhidden*o3>+B#style.visibility<*(4%(D' =%(pDg' =4@BBBB%()))D' =1:Bvisible*o3>+B#style.visibility<*+4%(D' =-s6Bwipe(down)*<3<*+4D' =%(@D)' =4@BB BB%(D' =-g6B fade*<3<*+4D' =1:Bhidden*o3>+B#style.visibility<*+4%(D' =%('D9' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*)4%(D' =-u6Bwipe(right)*<3<*)4D' =%(.D)' =4@BB BB%(D' =-g6B fade*<3<*)4D' =1:Bhidden*o3>+B#style.visibility<*)4%(D' =%(6D7' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*,4%(D' =-s6Bwipe(down)*<3<*,4D' =%(>D)' =4@BB BB%(D' =-g6B fade*<3<*,4D' =1:Bhidden*o3>+B#style.visibility<*,4%(Dp ' =%(PFD3' =4@BB BB%(D' =1:Bvisible*o3>+B#style.visibility<*(4%(D' =-o6Bdissolve*<3<*(4Dg' =4@BBBB%()))D' =1:Bvisible*o3>+B#style.visibility<*+4%(D' =-s6Bwipe(down)*<3<*+4D3' =4@BB BB%(D' =1:Bvisible*o3>+B#style.visibility<*,4%(D' =-o6Bdissolve*<3<*,4D3' =4@BB BB%(D' =1:Bvisible*o3>+B#style.visibility<*)4%(D' =-o6Bdissolve*<3<*)4D)' =%(D' =%(Dy' =4@BB5BB%()))D' =1:Bvisible*o3>+B#style.visibility<*4%(D' =+4 8?RCBBCB#ppt_wB*Y3>B ppt_w<*4D' =+4 8?RCBBCB#ppt_hB*Y3>B ppt_h<*4D' =-g6B fade*<3<*4+8+0+'40 +M= 0N0 //88^/(  8x 8 c $4 t `  t  280 c $0e0eA     ? A@  AjJ 8c8c     ?1 d0u0@Ty2 NP'p<'pA)BCD|E||s " 0e@        @ABC DEEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abN E5%  N E5%  N F   5%    !"?N@ABC DEFFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `ab` P H $D 0 t 480 c $0e0eA     ? A@  AjJ 8c8c     ?1 d0u0@Ty2 NP'p<'pA)BCD|E||s " 0e@        @ABC DEEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abN E5%  N E5%  N F   5%    !"?N@ABC DEFFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `ab` 0 X H  $D 0 tk 8 N"t jJ?"6@ NNN?NP qFind the lengths of the segments. Tell whether any of the segments have the same length. Click for each answer."r 2[ %8 NT(t jJ?"6@ NNN?NP @  7y(28 @  08@ B 8  `DjJ?"0@NNN?N@ @ B 8  fDjJ?"0@NNN?N  B 8 ZDo?"0@NNN?N` B 8B ZD|o?"0@NNN?N` B 8 ZD*o?"0@NNN?N @ B 8 TDjJ?"0@NNN?N p B  8 ZDjJ?"0@NNN?N` ` 0  #8 Tt jJ?"6@ NNN?NP   51(2 $8 T1t jJ?"6@ NNN?N  51(2 &8 T 5t jJ?"6@ NNN?N  7x(22 '8 ZjJ?"6@ NNN?N2 (8 ZjJ?"6@ NNN?NE u 2 )8 ZjJ?"6@ NNN?N 2 *8 ZjJ?"6@ NNN?N(  X 8  +8 T9t jJ?"6@ NNN?N0  TE(-3, 3)0 (2 ,8 T?t jJ?"6@ NNN?N@   TG(-3, 0)0 (2 -8 TDDt jJ?"6@ NNN?N@ p SF(1, 2)0(2 .8 TIt jJ?"6@ NNN?N p  TH(0, -1)0 (2 680 c $0e0eA     ? A@  AjJ 8c8c     ?1 d0u0@Ty2 NP'p<'pA)BCD|E||s " 0e@        @ABC DEEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abN E5%  N E5%  N F   5%    !"?N@ABC DEFFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `ab` X H $D 0 tN 88 NRt jJ?"6@ NNN?N P,$ 0 ^*None of the segments have the same length.+ 2+H 8 0޽h ? 33  ___PPT10 .avm+Dw '  = @B D2 ' = @BA?%,( < +O%,( < +D' =%(D' =%(D7' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*28%(D' =-s6Bwipe(left)*<3<*28D' =%(D' =%(D7' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*48%(D' =-s6Bwipe(left)*<3<*48D' =%(D' =%(D7' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*68%(D' =-s6Bwipe(left)*<3<*68D' =%(DD' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*88%(D' =-s6Bwipe(left)*<3<*88+8+0+880 +7 0N0 9-1-.<,(  < &< Njt jJ?"6@ NNN?N   JClick for each answer. 2x < c $Xmt `  t  '<0 c $0e0eA     ? A@  AjJ 8c8c     ?1 d0u0@Ty2 NP'p<'pA)BCD|E||s " 0e@        @ABC DEEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abN E5%  N E5%  N F   5%    !"?N@ABC DEFFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `ab @H $D 0 t +<0 c $0e0eA     ? A@  AjJ 8c8c     ?1 d0u0@Ty2 NP'p<'pA)BCD|E||s " 0e@        @ABC DEEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abN E5%  N E5%  N F   5%    !"?N@ABC DEFFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abX  H $D 0 t < N,pt jJ?"6@ NNN?N  `.Find the distance between each pair of points./ 2/8   %< B  <  `DjJ?"0@NNN?N@ @ B  <  `DjJ?"0@NNN?NppB < TDjJ?"0@NNN?N Gp GB < ZDjJ?"0@NNN?N` 7`  < Tvt jJ?"6@ NNN?NP   51(2 < Tzt jJ?"6@ NNN?N g  51(2 < Tgt jJ?"6@ NNN?N 7W  7x(22 < ZjJ?"6@ NNN?N D2 < ZjJ?"6@ NNN?N  2 < ZjJ?"6@ NNN?N( o X  < Tt jJ?"6@ NNN?N@` ` TK(-2, 2)0 (2 < TXt jJ?"6@ NNN?N 0 0  U L(-2, -3)0 (2 < Tt jJ?"6@ NNN?N W pw  TM(0, -1)0 (2B  < NDo?"0@NNN?N 0@ B !<B TD*3o?"0@NNN?N @ B "< TD2$o?"0@NNN?N 0  $< NPt jJ?"6@ NNN?N @  7y(2 -<0 c $0e0eA     ? A@  AjJ 8c8c     ?1 d0u0@Ty2 NP'p<'pA)BCD|E||s " 0e@        @ABC DEEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abN E5%  N E5%  N F   5%    !"?N@ABC DEFFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `ab H  $D 0 tH < 0޽h ? 33'  ___PPT10 .av+zD '  = @B D ' = @BA?%,( < +O%,( < +D' =%(D' =%(D7' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*'<%(D' =-s6Bwipe(left)*<3<*'<D' =%(D' =%(D7' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*+<%(D' =-s6Bwipe(left)*<3<*+<D' =%(D' =%(D7' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*-<%(D' =-s6Bwipe(left)*<3<*-<+|;  0N0 p (     0@tS"  `}  t :  NTt jJ?"6@ NNN?N` ,$ 0 Jcongruent segments 2*&  T8t ?"6@`NNN?N,$D 0 0bImportant: Segments are NOT equal; they are congruent. Congruent segments have equal lengths. : 2)(2 +  0p  # x ,$D0B  <Do?"0@NNN?NP B   <Do?"0@NNN?N P    Bt jJ?"6@ NNN?N0p  5M 2   Bt jJ?"6@ NNN?N  5N 2   BXt jJ?"6@ NNN?N` p  5P 2   Bt jJ?"6@ NNN?NP   5Q 2"    # @ @` ,$D 0  Ht jJ?"6@ NNN?N   > Incorrect: 2  2  F0e0eA -    ? A@  AjJ 8c8c     ?A)BCD|E||# "0e@       @ABC DEEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abN E5%  N E5%  N F   5%    !"?N@ABC DEFFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `ab  - t 0  F0e0eA /    ? A@  AjJ 8c8c     ?A)BCD|E||# "0e@       @ABC DEEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abN E5%  N E5%  N F   5%    !"?N@ABC DEFFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `ab   H /$D 0 t0  H(t jJ?"6@ NNN?N p0 ,$ 0 FCorrect:" 2T2  Tt8c?"6@`NNN?N@y,$D0 ^$Be sure you understand this concept!%(2%H  0޽h ? 33___PPT10.h|ô+tD' t= @B D' = @BA?%,( < +O%,( < +D' =%(D' =%(DD' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-s6Bwipe(left)*<3<*Du' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =+4 8?RCBBCB#ppt_wB*Y3>B ppt_w<*D' =+4 8?RCBBCB#ppt_hB*Y3>B ppt_h<*D' =+K4 8?CBB#ppt_x+(cos(-2*pi*(1-$))*-#ppt_x-sin(-2*pi*(1-$))*(1-#ppt_y))*(1-$)CB?B*Y3>B ppt_x<*D' =+K4 8?CBB#ppt_y+(sin(-2*pi*(1-$))*-#ppt_x+cos(-2*pi*(1-$))*(1-#ppt_y))*(1-$)CB?B*Y3>B ppt_y<*DN' =%(D' =%(D3' =4@BB BB%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-o6Bdissolve*<3<*D' =%(D7' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-s6Bwipe(left)*<3<*D' =%(Dt' =A@BBBB0B%()))D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-s6Bwipe(left)*<3<*D' =%(D' =%(D7' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-s6Bwipe(left)*<3<*D' =%(D' =%(DV' =A@BB5BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =+4 8?RCBBCB#ppt_wB*Y3>B ppt_w<*D' =+4 8?RCBBCB#ppt_hB*Y3>B ppt_h<*D' =-g6B fade*<3<*++0+0 ++0+0 ++0+0 ++0+0 +h  0N0 GG#2G(  x  c $ t` `m  t  0 s *0e0eA 2    ? @  jJ 8c8c     ?1 d0u0@Ty2 NP'p<'pA)BCD|E||s " 0e@        @ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abN 5%  N 5%  N    5%    !"?N@ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `ab 2 t F `0   P   Nxt jJ?"6@ NNN?N`0PP 7y(2  Nt jJ?"6@ NNN?N   7x(2B   `DjJ?"0@NNN?N` B   `DjJ?"0@NNN?N @ B  NDo?"0@NNN?N@ _   Nt jJ?"6@ NNN?N   B(x1, y1)v 2**_   N jJ?"6@ NNN?Np  A(x2, y2)v 2**2   NjJ?"6@ NNN?Nu  2   NjJ?"6@ NNN?N(X  B  jJ?"6@ NNN?N  SClick to form a right triangle. 2 B  <DԔ?"0@NNN?N` 0`,$@ 0B  <DԔ?"0@NNN?N00`,$@ 0~  N jJ?"6@ NNN?N` ,$0 (x2, y1)j 2**1l @ "E,$D0  B jJ?"6@ NNN?N @ ?C" 22 ! HjJ?"6@ NNN?NKJ # B jJ?"6@ NNN?NP,$ 0 fWhat are the coordinates of C?, 2 %0  @0e0eA 3    ? A@  AjJ 8c8c     ?A)BCD|E||# "0e@       @ABC DEEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abN E5%  N E5%  N F   5%    !"?N@ABC DEFFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `ab  H 3$D 0 @ ' B(! jJ?"6@ NNN?N @ ,$ 0 \*Square both sides of the distance formula:+ 2+Sl @P  +P@ ,$D 0 ( B% jJ?"6@ NNN?N` 5a 2 ) B) jJ?"6@ NNN?N`  5b 2 * B- jJ?"6@ NNN?N@P0p 5c 2l  0  10  ,$D  0 $ B2 jJ?"6@ NNN?N 0   From the Ruler Postulate, we also know that BC = x2  x1 and AC = y2  y1 . Then by substitution we know that c2 = a2 + b2. This is known as the Pythagorean Theorem. More in Chapter 9!$ 2    "   A @ P ( 0P ( , c 0e0e    BCDEF AjJ 8c8c     ?A)BCD|E||@s "0e@    @ABC DEEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abN E5%  N E5%  N F   5%    !"?N@ABC DEFFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abt u( - s 0e0e    BCDEF jJ 8c8c     ?A)BCD|E||@s "0e@    @ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abN 5%  N 5%  N    5%    !"?N@ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `ab ( . s 0e0e    BCDEF jJ 8c8c     ?A)BCD|E||@s "0e@    @ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abN 5%  N 5%  N    5%    !"?N@ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abP Q ( / s 0e0e    BCDEF jJ 8c8c     ?A)BCD|E||@s "0e@    @ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abN 5%  N 5%  N    5%    !"?N@ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `ab (| 2 NQo?"0@NNN?N0 @P ,$  0 JLet s say AB= c, BC = a, and AC = b. ,& 2 H  0޽h ? 33  ___PPT10 .hÌ+OD' B= @B Dl' = @BA?%,( < +O%,( < +D]' =%(D' =%(D7' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-s6Bwipe(left)*<3<*D3' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-o6Bwipe(up)*<3<*D3' =4@BB BB%(D' =1:Bvisible*o3>+B#style.visibility<*"%(D' =-o6Bdissolve*<3<*"D{' =%(D#' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*#%(D' =+4 8?dCB1+#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*#D' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*#D' =%(D' =%(DV' =A@BB5BB0B%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =+4 8?RCBBCB#ppt_wB*Y3>B ppt_w<* D' =+4 8?RCBBCB#ppt_hB*Y3>B ppt_h<* D' =-g6B fade*<3<* D' =%(D' =%(DD' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*'%(D' =-s6Bwipe(left)*<3<*'D' =%(D7' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*%%(D' =-s6Bwipe(left)*<3<*%D/' =%(D' =%(DD' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*2%(D' =-s6Bwipe(left)*<3<*2D3' =4@BB BB%(D' =1:Bvisible*o3>+B#style.visibility<*+%(D' =-o6Bdissolve*<3<*+D' =%(D' =%(D3' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*1%(D' =-o6Bwipe(up)*<3<*1++0+ 0 ++0+#0 ++0+'0 ++0+20 +E 0N0 aY!<4 (  B  NDo? "0@NNN?N ,$D  0B 3 ZDԔ? "0@NNN?N ,$D 0B 4 ZDԔ? "0@NNN?N,$D 0 5 NHgo?"0@NNN?N $ 0LD___PPT9& f What would the distance be if a diagonal street existed between the two points? Solution:@X! 2 2X8XL @  # %N   0    0N   0    0n  0"`> 0n2  0"` 00n2   0"` 0   0wk  A EXAMPLE 4 2 Z   C *Aj0311784@   By ` P<$0   \  B4|Ԕ?"6@ NNN?N ` X,$D0 x Study Example 4 before going on!<!(2n  B jJ?"6@ NNN?N8 ,$0 XOn the map, the city blocks are 410 feet apart east-west and 370 feet apart north-south.Y 2YT l  0`0  90 `0 ,$D0  ! H\o? "0@NNN?N @ S C(0, 740). 2 $ Ho? "0@NNN?N`0  W D(2050, -370). 2 &@  0p  6 0p   H4o? "0@NNN?N   7y(2B  NDo? "0@NNN?N 0 B  ZDo? "0@NNN?N @  H$o? "0@NNN?Np 7x(2B ' NDo? "0@NNN?N;   ( Ho? "0@NNN?N d K 5370 2B ) NDo? "0@NNN?N` ` P * Ho? "0@NNN?Nm 5M  7- 410 22  To? "0@NNN?Nf  2  To? "0@NNN?N  / Bo?"0@NNN?N  t$0@8___PPT9 6Find the walking distance between C and D. Solution:F+ 2 2"8X ; c $A d?? @ 8 d$D  0 < c $A g?? @X8 g$D  0H  0޽h ? 33))___PPT10).pRy+ZE D('  = @B DL(' = @BA?%,( < +O%,( < +Db' =%(D ' =%(D' =A@BB3BB0B%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =-g6B fade*<3<* )?D' =0l9 BB A AHCC*<3<* )?D' =0l9 BBHCCBB*<3<* %()?D' =1:B (0.5)*Y3>B ppt_x<* D ' =+4 . B (0.5)0B(#ppt_x)*Y3>B ppt_x<* %()?D' =1:B(#ppt_y+0.4)*Y3>B ppt_y<* D' =+4 . B(#ppt_y+0.4)0B(#ppt_y)*Y3>B ppt_y<* %()?D ' =%(DW' =%(D' =A@BB"BB0B%(D' =1:Bvisible*o3>+B#style.visibility<* %(D ' X=+4 . B(-#ppt_w/2)0B(#ppt_x)*Y3>B ppt_x<* %(D' =+4 . B00B -1.0*[3>Bxshear<* %(X))?)?D' =0l9 BBBBBB*<3<* %(X))?)?D2' =+4 )B-(#ppt_h/3+#ppt_w*0.1)*Y3>B ppt_x<* %(X))?)?D' =%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-o6Bdissolve*<3<*D3' =4@BB BB%(D' =1:Bvisible*o3>+B#style.visibility<*9%(D' =-o6Bdissolve*<3<*9D' =%(D' =%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*/%(D' =-o6Bdissolve*<3<*/D' =%(D7' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*3%(D' =-s6Bwipe(left)*<3<*3D' =%( D3' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*4%(D' =-o6Bwipe(up)*<3<*4D' =%(D' =%(D7' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*;%(D' =-s6Bwipe(left)*<3<*;D' =%(D' =%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*5%(D' =-o6Bdissolve*<3<*5D' =%(D7' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-s6Bwipe(left)*<3<*D' =%(D' =%(D7' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*<%(D' =-s6Bwipe(left)*<3<*<++0+50 ++0+ 0 ++0+ 0 ++0+0 ++0+/0 +R 0N0 " (  r  S |΀     88  p  ! p  @  p   p S @ @p  @p pN  pP    pP N  pP    pP   H|рo?"0@NNN?N   7y(2B   NDo?"0@NNN?N ` P B   ZDo?"0@NNN?N `@`B  NDo?"0@NNN?N` `    HPրo?"0@NNN?N@p` 7x(22  To?"0@NNN?ND t 2  To?"0@NNN?NHx   HԀo?"0@NNN?N0 S E(820, 0). 2  H,߀o?"0@NNN?N@  XF(-410, -1110). 2 B  NDo?"0@NNN?N; @ @  Ho?"0@NNN?N   5370 2B  NDo?"0@NNN?N` 0`   Ho?"0@NNN?Nm M  7- 410 2N  Bo?"0@NNN?N p \ >Find the diagonal distance between points E and F on the map. B? 2*   Bo?"0@NNN?NP   = Answer:  2 # " Bo?"0@NNN?N  ,$ 0 E about 1657 ft 2H  0޽h ? 33ME___PPT10%.h6+'"D' = @B D|' = @BA?%,( < +O%,( < +D' =%(D[' =%(D' =A@BBBB0B%()))D' =1:Bvisible*o3>+B#style.visibility<*"%(D' =+4 8?dCB1+#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*"D' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<*"+8+0+"0 + 0N0 2(    N o?"0@NNN?N  D QUESTIONS? 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D(02 "Segments and Their Measures.-v:--*$ 4 3 20., * ) )))*,.0234 4----*% 4 3 20., * ) )))*,.0234 4--'@Arial-.  2 1 GOAL.---6$ (((),-.01345 5!5"4$3&1&0&.&-&,$)"(!( (----6% (((),-.01345 5!5"4$3&1&0&.&-&,$)"(!( (--'@Arial-.  2 11!.-@Arial-. (2 1(Use Segment Postulates.-v:--*$ E D CB@> < ; ::;<>@BCDE E----*% E D CB@> < ; ::;<>@BCDE E--'@Arial-.  2 B GOAL.---6$ 999;=>@ABDFF F!F#F%D&B'A'@'>&=%;#9!9 9----6% 999;=>@ABDFF F!F#F%D&B'A'@'>&=%;#9!9 9--'@Arial-.  2 B2!.-@Arial-. =2 @)$Use the Distance Formula to measure .-@Arial-. 2 F) distances.-@BBradley Hand ITC-. D( 2 # What.-@BBradley Hand ITC-. 2 #you should learn.-@Arial-. 2 Z To solve reala.-@Arial-.  2 Z0-!.-@Arial-. E2 Z2)life problems, such as finding distances .-@Arial-. 32 `along a diagonal city street..-2$-- $ Z VV---- $ Z VV--'@BBradley Hand ITC-. D( 2 Q Why .-@BBradley Hand ITC-. $2 Qyou should learn it.-՜.+,0|    On-screen Showusd410 ArialBradley Hand ITCVerdanaTimes New RomanDefault DesignMathType 5.0 EquationSlide 1Slide 2POSTULATES YOU NEED TO KNOWExtra Example 1Slide 5Extra Example 2 CheckpointSlide 8Slide 9Extra Example 3 CheckpointTOf course, some segments have equal lengths. These are called _________________. 0Now lets look again at the Distance Formula. Extra Example 4 Checkpoint Slide 16  Fonts UsedDesign TemplateEmbedded OLE Servers Slide Titles_Պhb2006hb2006  !"#$%'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~      !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~ Root EntrydO)PicturesKCurrent UserSummaryInformation(PowerPoint Document(&DocumentSummaryInformation8