GSP4 yQThat document was created with a newer version of Sketchpad and cannot be opened.|This document was created with a newer version of Sketchpad. Some information may be lost. The document will open as a copy.$BLInitial Page` a b c d e f g h i j k l m n o p q _ ,#GSP4_W_0554/Mar 2 20040#` Ariale ArialeTimes New Roman$    '''$'$'$'$'s$'$'$'$'$'$' $' $' %'&'8'8'8'9':' ,,  ?8 Am@0v@@C8{w@vcrz"s@@ @B }@@v@@ @ @ @ @ /@  /@   -@  D  .   -  E    @  / /  - F .  - G5  . .  - H   @  / #/ # - $"I &. &# - %(5)& &) ). &. '    &5 &5shhT>nQ\aAt[1] nn 4 n5n 46 -n 7O Cn786 9 C]?>  :   n$nQ\aA Move Point> n :9   &nQ\aA Show Objects> n:$> @F    &nQ\aA Animate Point4n4)>  =;   d8(nQ\aAAnimate Point Cn0.>>[! n   y2nQ\aA-->>4 Congruent Trianglesy#(#@QThat document was created with a newer version of Sketchpad and cannot be opened.|This document was created with a newer version of Sketchpad. Some information may be lost. The document will open as a copy.$aELShowing 4 Congruent Triangles` a b c d e f g h i j k l m n o p q _ ,#GSP4_W_0554/Mar 2 20040#` Arial    '''$'$'$'$'$'$'$'$'$'$' $' $' %'&'8'8'8'9':' 00>w- Am@0v@@C`w@q@@ @B }@0v@@ @ @ @ @ /@  /@   -@  D  .   -  E    @  / /  - F .  - G5ٵ  . .  - H   @  / #/ # - $"I &. &# - %(5ٵ)& &) ). &. '    &5 &5hhT>nQ\aAt[1]nK[@z@@p@z@@ 45 @6 f?J%0 74  <0>K5F 28K?K5F 18K?> 7$> @F   &nQ\aA Animate Point4n4)> :9*   ,nQ\aAHide Quadrilaterals4n 4 &> '!    &nQ\aA Show Segments> n ?@   (nQ\aAShow Trianglesr> n >B   16nQ\aAShow Four Congruent Triangles> n B>   XFnQ\aAReSet n   5&6nQ\aA-->>Translate Triangles Only5&8QThat document was created with a newer version of Sketchpad and cannot be opened.|This document was created with a newer version of Sketchpad. Some information may be lost. The document will open as a copy.$ZLTranslate Triangles Only` a b c d e f g h i j k l m n o p q _ ,#GSP4_W_0554/Mar 2 20040#` Arial    '''$'$'$'$'$'$'$'$'$'$' $' $' %'&'8'8'8'9':' 00>- Am@y@@CPx@v@@ @B }@ y@@ @ @ @ @ /@  /@   -@  D  .   -  E    @  / /  - K .  - G  . .  - H   @  / "/ " - #!J %. %" - $' %( (. %. &    %5nQ\aAKn@e@@0 0 %I 01 12 02 - &nQ\aAJn0 6 724ٵ7214072 65ٵ(6 -  nQ\aAL5n= 65ٵ= =nQ\aAMn@e@@A A F BA BC CAA = CG4CAG4ٵGCB> C2%   HnQ\aAReset> n2C   (,nQ\aATranslate Trianglesn9>>>9jnhhT>nQ\aAt[1]l> n>I:/   ,nQ\aAHide Parallelograms> n?J<9   ~&nQ\aA Hide Squareso4n0214BCA>  QR   (nQ\aAShow Trianglesr> n ;@8H   &nQ\aA Show Segments> n   z,nQ\aAShow Intersection G> nOPS    *nQ\aAHideParSqrShowTri> nSPO   Xc(nQ\aAResetTriSqrParr4n4(    P 0nQ\aA-->>Translate TrianglesP QThat document was created with a newer version of Sketchpad and cannot be opened.|This document was created with a newer version of Sketchpad. Some information may be lost. The document will open as a copy.$([LTranslate Triangles` a b c d e f g h i j k l m n o p q _ ,#GSP4_W_0554/Mar 2 20040#` Arial Times New Roman   '''$'$'$'$'$'$'$'$'$'$' $' $' %'&'8'8'8'9':' 00>w- Am@y@@Cw@pu@@ @B }@ y@@ @ @ @ @ /@  /@   -@  D  .   -  E    @  / /  - K .  - G  . .  - H   @  / "/ " - #!J %. %" - $' %( (. %. &    %5nQ\aAKn@e@@0 0 %I 01 12 02 - &nQ\aAJn0 6 724ٵ7214072 65ٵ(6 -  nQ\aAL5n= 65ٵ= =nQ\aAMn@e@@A A F BA BC CAA = CG4CAG4ٵGCB> C2%   HnQ\aAReset> n2C   (,nQ\aATranslate Trianglesn9>>>9jnhhT>nQ\aAt[1]l> n>I:/   ,nQ\aAHide Parallelograms> n?J<9   ~&nQ\aA Hide Squareso4n0214BCA>  QR   (nQ\aAShow Trianglesr> n ;@8H   &nQ\aA Show Segments> n   z,nQ\aAShow Intersection G> nOPS    *nQ\aAHideParSqrShowTri> nSPO   XO(nQ\aAResetTriSqrParr4n4(>4    +4nQ\aA-->>Two (2) Parallelograms+ QThat document was created with a newer version of Sketchpad and cannot be opened.|This document was created with a newer version of Sketchpad. Some information may be lost. The document will open as a copy.$@LShowing Two Parallelograms` a b c d e f g h i j k l m n o p q _ ,#GSP4_W_0554/Mar 2 20040#` Arial Times New Roman   $'''$'$'$'$'$'$'$'$'$'$' $' $' %'&'8'8'8'9':' 00>- Am@0v@@Cx@s@@ @B }@@v@@ @ @ @ @ /@  /@   -@  D  .   -  E    @  / /  - F .  - G5ٵ  . .  - H   @  / #/ # - $"I &. &# - %(5ٵ)& &) ). &. '    &5 &5hhT>nQ\aAt[1]nKЃ@J@@@J@@ 45 @6 oy%W?J%0 74  G<0>K5 28K?K5 18K?> 7$> @F   -&nQ\aA Animate Point4n4)> 45678   &nQ\aA Show ObjectsnP>Ps n   W*"nQ\aA -->>ProofW*<QThat document was created with a newer version of Sketchpad and cannot be opened.|This document was created with a newer version of Sketchpad. Some information may be lost. The document will open as a copy.$ pLProof` a b c d e f g h i j k l m n o p q _ ,#GSP4_W_0554/Mar 2 20040#` Arial Times New Roman   $'''$'$'$'$'$'$'$'$'$'$' $' $' %'&'8'8'8'9':' 00>w Am@y@@Cw@Pu@@ H0~n?b0B }@y@@ \b?a\ >c8Z?cc @ c /c  /c   -c  D  .   -  E   ?c @  / /  - K .  - G  . .  - H t?b  @  / "/ " - #!J %. %" - $' %( (uQ?a. %. &    %5nQ\aAKn@e@@0 0 %I 01 12 02 - &nQ\aAJn0 6 724ٵ7214072 65ٵ(6 -  nQ\aAL5n= 65ٵ= =nQ\aAMn@e@@A A F BA BC CAA = CG4CAG4ٵGCB> C2%   |nQ\aAReset> n2C   ,nQ\aATranslate Trianglesn9>>>9jnhhT>nQ\aAt[1]l> n>I:/   ,nQ\aAHide Parallelograms> n?J<9   ~&nQ\aA Hide Squareso4n0214BCA>  QR   (nQ\aAShow Trianglesr> n ;@8H   &nQ\aA Show Segments> n   z,nQ\aAShow Intersection G> nOPS    *nQ\aAHideParSqrShowTri> nSPO   XO(nQ\aAResetTriSqrParr4n4( >F0x  u<+><+><+>>> '/  - \J ][Ͷ;@?hDBO/>O3mtrx_<+><+><+>>>x@@->>>hhT>>>>44 >>x.LL8>>$44/ >>x/Mtt`a<+><+><+>>>`T>  ^]   1*nQ\aAHide Altitude 'h'> n_   EVnQ\aA1> n`   E{nQ\aA2> nb   DnQ\aA3> n ac   FnQ\aA4> nd   A nQ\aA5> ne   @3nQ\aA6> nf   ?QnQ\aAConcA> n$_`bacdef   (nQ\aAHide All Stepsh n    0nQ\aA-->>C is a Right Anglea IQThat document was created with a newer version of Sketchpad and cannot be opened.|This document was created with a newer version of Sketchpad. Some information may be lost. The document will open as a copy.$MLWhen C is a Right Angle` a b c d e f g h i j k l m n o p q _ ,#GSP4_W_0554/Mar 2 20040#` Arial Times New Roman    '''$'$'$'$'t$'$'$'$'$'$' $' $' %'&'8'8'8'9':' 00>- Am@0v@@B }@0v@@ @ @ @ /@ /@  -@ D  .   -  E    hhT>nQ\aAt[1] nn  nn  -n O Cn  Cj?>     &nQ\aA Show Objectsg> n$> @F   &nQ\aA Animate Pointn00>w~!n O CnC\ѡZu@CyHq@4@>     p$nQ\aA Move Pointn> n    d (nQ\aAAnimate Point C@ n /n  /n  n  -n "#F $ . $  - !&G '. ( $'5'$ $ . '- - ).H5t'/@  /'/ /1/ '1 '/ - 34I5$ 5'  5. 5*. 51 - 294/: :/ 5:5:5'/ '5. $? /' /   C rO?> D$> @F   4q4nQ\aAAnimate Point on SemiCircle> n D   2$nQ\aA Move Pointn> n EF   XNnQ\aA4Presentation: Didn't work 'cause point was on circlenD<?rV??ause poi>  H   3$nQ\aA Move Point> nGEI   X0nQ\aAWhen C is a right angle> nH   +:nQ\aA Show Point (1 Pixel Translation)pn<+><+><+>><0>>> n   .nQ\aA-->>When C Lies on AB='QThat document was created with a newer version of Sketchpad and cannot be opened.|This document was created with a newer version of Sketchpad. Some information may be lost. The document will open as a copy.$GLWhen C Lies on AB` a b c d e f g h i j k l m n o p q _ ,#GSP4_W_0554/Mar 2 20040#` Arial Times New Roman     '''$'$'$'$'v$'$'$'$'$'$' $' $' %'&'8'8'8'9':' 00>J% Am@0v@@C 5ňw@q@@ @B @0v@@ @ @ @ @ /@  /@   -@  D  .   -  E    @  / /  - F .  - G5  . .  - H   @  / #/ # - $"I &. &# - %(5)& &) ). &. '    &5 &5vhhT>nQ\aAt[1] nn 4 n5n 46 -n 7O Cn786 9 Cj?>  :   p$nQ\aA Move Point> n :9   &nQ\aA Show Objectse> n:$> @F   &nQ\aA Animate Point4n4)>  =;   d(nQ\aAAnimate Point Cn((>g! n (=m?> nB$> @F   L,nQ\aAAnimate Point on AB> n B   ,nQ\aAMove Point C to AB> n CD   X.nQ\aAAnimate Point C on ABn``gM><+>>>><+><+>>><0><+>>>>><0>>>g)- n   (nQ\aA-->>Tesselation<&QThat document was created with a newer version of Sketchpad and cannot be opened.|This document was created with a newer version of Sketchpad. Some information may be lost. The document will open as a copy.$G LTesselation` a b c d e f g h i j k l m n o p q _ ,#GSP4_W_0554/Mar 2 20040#` Arial  '''$'$'$'$'$'$'$'$'$'$' $' $' %'&'8'8'8'9':' nQ\aAD}@{@@nQ\aAF}@s@@ @ @ @ /@ /@  -@ nQ\aABn .n  -n  nQ\aAAn  n  n                                               ! " # $ % & ' ( ) * + , - . / 0 1 2 3 4 5 6 7 8 9 : ; < = > ? @ A B C D E F G H I J K L M N O P Q R S T U V W X Y Z [ \ ] ^ _ ` a b c d e f g h i j k l m n o p q r s t u v w x y z { | } ~                     @{@@@p|@@  @x~ ?k8C                       @  / /   -                                                .  -                               @  /   -        " # $ % &  ( ) * + , ( . / 0 1 2 55454 56 57 58 59 54 5;5; 5= 5> 5? 5@ 54 5B5B 5D 5E 5F 5G 5B 5I5I 5K 5L 5M 5N  P Q R S T P V W X Y Z P \ ] ^ _ ` \ b c d e f  h i j k l h n o p q r h t u v w x t z { | } ~  -                        5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5                                                  5ٵ5ٵ 5ٵ 5ٵ 5ٵ 5ٵ 5ٵ 5ٵ 5ٵ 5ٵ 5ٵ 5ٵ 5ٵ 5ٵ 5ٵ 5ٵ 5ٵ 5ٵ 5ٵ 5ٵ 5ٵ 5ٵ 5ٵ 5ٵ  -   - nQ\aAE5ٵn5:5ٵ595ٵ585ٵ575ٵ565ٵ54                                ! "  $ % & ' (  * + , - . * 0 1 2 3 4  6 7 8 9 : 6 < = > ? @ 6 B C D E F B H I J K L  N O P Q R N T U V W X N Z [ \ ] ^ Z ` a b c d 5ٵ5ٵf5ٵf 5ٵh 5ٵi 5ٵj 5ٵk 5ٵf 5ٵm5ٵm 5ٵo 5ٵp 5ٵq 5ٵr 5ٵf 5ٵt5ٵt 5ٵv 5ٵw 5ٵx 5ٵy 5ٵt 5ٵ{5ٵ{ 5ٵ} 5ٵ~ 5ٵ 5ٵ                                                                          > $>@F    nQ\aAAnimaten    !"PV\bhntz55555ٵ5ٵ5ٵ5ٵ $*06<BHNTZ`555<5C5J55555ٵ5ٵ5ٵ5ٵ5ٵg5ٵn5ٵu5ٵ| !:<=VXYrtu5;5<5=5>5?5@5A5I5J5K5L5M5N5OVWXYZ[bcdefgnopqrsz{|}~5555555ٵ5ٵ5ٵ5ٵ5ٵ5ٵ5ٵ5ٵ5ٵ5ٵ5ٵ5ٵ  012345HIJKLM`abcde5ٵ{5ٵ|5ٵ}5ٵ~5ٵ5ٵ5ٵ55ٵ5ٵ55 5$(,5ٵ.5ٵ0248<@5ٵDHLhhT>nQ\aAt[1]tQThat document was created with a newer version of Sketchpad and cannot be opened.|This document was created with a newer version of Sketchpad. Some information may be lost. The document will open as a copy.$ 4LLaw Of Cosines[original]` a b c d e f g h i j k l m n o p q _ ,#GSP4_W_0554/Mar 2 20040#` Arial   '''$'$'$'$'$'$'$'$'$'$' $' $' %'&'8'8'8'9':' Aq@@q@@B@W@@q@@ DragMe!d@n@@PN':<0>>r' dh?c B!?a }A?b/ ?k  @1/ ?t  @3 -  C -  F/  ?m   @2  ?n/  ?u   @4  ?v.  ?z - D - G. ?a5` ?p6g  ?p ?q  ?w ?x - H ?e5 ?1*2  @b<0>m4g*2  A?<0>m2g/ ?m1g  ?b ?c  ?d.  ?f. ?g5`` ?4*2(  C<0>m5g - "K - &'J *ffffff?hf + ?h +?j1g + ?k1g5+  ?25``+ ?3*21  A<0>m6g*20  Bp<0>m3g0 3 32)j 8<0>T2or J0````$ Sum 4 areas