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S  0ԍ "^ `  >*  0hڍ "^   @*  0 "^ `  @*H  0޽h ? 3380___PPT10.]R Default Design0 p\*(  \ \ 0l P    X*  \ 0     Z* d \ c $ ?   \ 0  0  RClick to edit Master text styles Second level Third level Fourth level Fifth level!     S \ 6  _P   X*  \ 6  _    Z* H \ 0޽h ? 3380___PPT10.I!>0^N0   D 1 (  DF    qD   T  p` D#   p`" D 0v:  0 D 0 *k"` P <GOAL 2`2 D 0p` D 0P.k 91 2  D 61kp GDESCRIBING POLYGONS 2 @  D#  k ,$D 0N   0 D   0N   0 D   0n D 0"`> 0n2 D 0"` 00n2 D 0"` 0 D 0h7kk  A EXAMPLE 1 2 Z D C *Aj0311784@ F l& D l& D 0+B#style.visibility<*D %(D' =-s6Bwipe(left)*<3<*D D'' =%(D)'' =%(DI' =4@BB5BB%(D' =1:Bvisible*o3>+B#style.visibility<*D %(D' =+4 8?RCBBCB#ppt_wB*Y3>B ppt_w<*D D' =+4 8?RCBBCB#ppt_hB*Y3>B ppt_h<*D D' =-g6B fade*<3<*D DI' =4@BB5BB%(D' =1:Bvisible*o3>+B#style.visibility<*D%(D' =+4 8?RCBBCB#ppt_wB*Y3>B ppt_w<*DD' =+4 8?RCBBCB#ppt_hB*Y3>B ppt_h<*DD' =-g6B fade*<3<*DDI' =4@BB5BB%(D' =1:Bvisible*o3>+B#style.visibility<*D %(D' =+4 8?RCBBCB#ppt_wB*Y3>B ppt_w<*D D' =+4 8?RCBBCB#ppt_hB*Y3>B ppt_h<*D D' =-g6B fade*<3<*D DI' =4@BB5BB%(D' =1:Bvisible*o3>+B#style.visibility<*D '%(D' =+4 8?RCBBCB#ppt_wB*Y3>B ppt_w<*D 'D' =+4 8?RCBBCB#ppt_hB*Y3>B ppt_h<*D 'D' =-g6B fade*<3<*D 'DI' =4@BB5BB%(D' =1:Bvisible*o3>+B#style.visibility<*D';%(D' =+4 8?RCBBCB#ppt_wB*Y3>B ppt_w<*D';D' =+4 8?RCBBCB#ppt_hB*Y3>B ppt_h<*D';D' =-g6B fade*<3<*D';DI' =4@BB5BB%(D' =1:Bvisible*o3>+B#style.visibility<*D;G%(D' =+4 8?RCBBCB#ppt_wB*Y3>B ppt_w<*D;GD' =+4 8?RCBBCB#ppt_hB*Y3>B ppt_h<*D;GD' =-g6B fade*<3<*D;GDI' =4@BB5BB%(D' =1:Bvisible*o3>+B#style.visibility<*DGS%(D' =+4 8?RCBBCB#ppt_wB*Y3>B ppt_w<*DGSD' =+4 8?RCBBCB#ppt_hB*Y3>B ppt_h<*DGSD' =-g6B fade*<3<*DGSDI' =4@BB5BB%(D' =1:Bvisible*o3>+B#style.visibility<*DS[%(D' =+4 8?RCBBCB#ppt_wB*Y3>B ppt_w<*DS[D' =+4 8?RCBBCB#ppt_hB*Y3>B ppt_h<*DS[D' =-g6B fade*<3<*DS[DI' =4@BB5BB%(D' =1:Bvisible*o3>+B#style.visibility<*D[d%(D' =+4 8?RCBBCB#ppt_wB*Y3>B ppt_w<*D[dD' =+4 8?RCBBCB#ppt_hB*Y3>B ppt_h<*D[dD' =-g6B fade*<3<*D[dD' =%(Dz' =%(D"' =4@BB"BB%()))D' =1:Bvisible*o3>+B#style.visibility<*D%(D ' X=+4 . B(-#ppt_w/2)0B(#ppt_x)*Y3>B ppt_x<*D%(D' =+4 . B00B -1.0*[3>Bxshear<*D%(X))?)?D' =0l9 BBBBBB*<3<*D%(X))?)?D2' =+4 )B-(#ppt_h/3+#ppt_w*0.1)*Y3>B ppt_x<*D%(X))?)?+? 0^N0 220(M $ 2(    P 6|k    CExtra Example 1 @  & # po,$D0N   0 '    0N   0 (    0n )  0"`> 0n2 *  0"` 00n2 +  0"` 0 ,  0pkk  A EXAMPLE 2 2 Z -  C *Aj0311784@ : .  fPk o?"6@ NNN?N ` f4Identify the figures that are not polygons. Explain.5 25E*8  L 0HN  p 8  @P B 9  # lDo?"0@NNN?NppB : # lDo?"0@NNN?N pB ; # lDo?"0@NNN?N pB < B  fDo?"0@NNN?N   B =  # lDo?"0@NNN?N 0 B >   fDo?"0@NNN?N0 0B ?   fDo?"0@NNN?N   f@  p A :@  p 7  pB 0  # lDo?"0@NNN?NppB 1 # lDo?"0@NNN?N pB 2 # lDo?"0@NNN?N pB 3 B  fDo?"0@NNN?N   B 4  # lDo?"0@NNN?N 0 B 5   fDo?"0@NNN?N0 0B 6   fDo?"0@NNN?N   B @  # lDo?"0@NNN?N0  B  # l o?"6@ NNN?N@@4@ @ p  J   @ C  # l o?"6@ NNN?N@ p B D  # lDo?"0@NNN?N L L B F  # lDo?"0@NNN?Nv p6  G   0e0e    BC!DEF Ao 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 px  H   0e0e    BCQDEF Ao 8c8c     ?1 d0u0@Ty2 NP'p<'pA)BCD|E||Q@ "0e@     @ABC DEEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abN E5%  N E5%  N F   5%    !"?N@ABC DEFFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abH S &  I   0e0e    BCQDEF Ao 8c8c     ?1 d0u0@Ty2 NP'p<'pA)BCD|E||Q@ "0e@     @ABC DEEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abN E5%  N E5%  N F   5%    !"?N@ABC DEFFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `ab S ! K   fk o?"6@ NNN?Np EA B C D 2 M  fk o?"6@ NNN?NP`  ,$D 0 rB: two sides intersect only one other side C: the sides intersect more than two other sides, some at nonendpoints."s 2re H  0޽h ? 33i a ___PPT10A ._`+&~D ' = @B D ' = @BA?%,( < +O%,( < +D' =%(D' =%(D7' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*M +%(D' =-s6Bwipe(left)*<3<*M +D' =%(D' =%(D7' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*M +s%(D' =-s6Bwipe(left)*<3<*M +sD)' =%(D' =%(Dy' =4@BB5BB%()))D' =1:Bvisible*o3>+B#style.visibility<*& %(D' =+4 8?RCBBCB#ppt_wB*Y3>B ppt_w<*& D' =+4 8?RCBBCB#ppt_hB*Y3>B ppt_h<*& D' =-g6B fade*<3<*& + 0^N0 z+(    6D    CExtra Example 2 @  #  P,$D0N   0    0N   0    0n  0"`> 0n2  0"` 00n2  0"` 0  0k  A EXAMPLE 3 2 Z  C *Aj0311784@ b  # l  o?"6@ NNN?N) JIdentify the polygon and state whether it is convex or concave. a. b."K 2@ 8 `p "`pB B # lDo?"0@NNN?N`B  # lDo?"0@NNN?NpB   # lDo?"0@NNN?N@pB ! # lDo?"0@NNN?N`@t8 @`0 )`@0B #  fDo?"0@NNN?N@`@@B $  fDo?"0@NNN?N@@0B &  fDo?"0@NNN?N`0B 'B  fDo?"0@NNN?N`B ( # lDo?"0@NNN?N@`] *  fx o?"6@ NNN?N @@ @,$ 0 Ua. convex quadrilateral" 2Y +  f@ o?"6@ NNN?N  @,$ 0 Qb. concave pentagon" 2H  0޽h ? 33  ___PPT10 ._`+u=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<*+D)' =%(D' =%(Dy' =4@BB5BB%()))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<*+p+0+*0 ++0++0 +' 0^N0 d\!0 (      6"    CExtra Example 3M    fX& o?"6@ NNN?N `Y y1Decide whether the polygon is regular. a. b.,2 2' T 8 0   `@B    fDo?"0@NNN?N`pB    fDo?"0@NNN?N ` pB    fDo?"0@NNN?Np p   # l o?"6@ NNN?N p   # l o?"6@ NNN?N pB   # lDo?"0@NNN?NppB    fDo?"0@NNN?N@B  B  fDo?"0@NNN?N`B    fDo?"0@NNN?N `B   # lDo?"0@NNN?NPPB   # lDo?"0@NNN?NP0 PB   # lDo?"0@NNN?N @pB  B # lDo?"0@NNN?N@@pt 8 @k . @k   # l o?"6@ NNN?N0    f o?"6@ NNN?N0 !   f o?"6@ NNN?N 0 "  # l o?"6@ NNN?NP #  # l o?"6@ NNN?N PB &  # lDo?"0@NNN?N@B '  # lDo?"0@NNN?N @ @` * @kB %  # lDo?"0@NNN?N`B (  # lDo?"0@NNN?N@@`N @` +  @/B ,  # lDo?"0@NNN?N`B -  # lDo?"0@NNN?N@@`h /   f3 o?"6@ NNN?Np@ v ,$0 `0a. No; all angles do not have the same measure.11b 0   f 8 o?"6@ NNN?Np` v ,$0 Z*b. No; all sides are not the same length.++H   0޽h ? 33  ___PPT10 ._`+4D" ' ;= @B D ' = @BA?%,( < +O%,( < +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' =%(DV' =A@BB5BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*0 %(D' =+4 8?RCBBCB#ppt_wB*Y3>B ppt_w<*0 D' =+4 8?RCBBCB#ppt_hB*Y3>B ppt_h<*0 D' =-g6B fade*<3<*0 +p+0+/ 0 ++0+0 0 + 0^N0 tl (  ~  s *A `      f@C o?"6@ NNN?N State whether the figure is a polygon. If it is, state whether it is convex or concave. If it is not a polygon, explain why not. 2C8 0   p"  3 rZ o?"6@ NNN?N0    fI o?"6@ NNN?N@ 7A(2y8  P  p@ P  PPB  # lDo?"0@NNN?N0B  # lDo?"0@NNN?N @B B  fDo?"0@NNN?N0@B   fDo?"0@NNN?N @ 0B  # lDo?"0@NNN?N@0B B # lDo?"0@NNN?N0 PB   fDo?"0@NNN?N0PB  # lDo?"0@NNN?NPP   fP o?"6@ NNN?N ` 7B(2   fS o?"6@ NNN?N` @ L ,$0 |4A: not a polygon because some sides are not segments,5(24`    fX o?"6@ NNN?N` @ ,$0 XB: concave octagon* 23333H  0޽h ? 33  ___PPT10 .av+zD" ' Z= @B D ' = @BA?%,( < +O%,( < +D' =%(D' =%(DV' =A@BB5BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =+4 8?RCBBCB#ppt_wB*Y3>B ppt_w<*D' =+4 8?RCBBCB#ppt_hB*Y3>B ppt_h<*D' =-g6B fade*<3<*D' =%(D' =%(DV' =A@BB5BB0B%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =+4 8?RCBBCB#ppt_wB*Y3>B ppt_w<* D' =+4 8?RCBBCB#ppt_hB*Y3>B ppt_h<* D' =-g6B fade*<3<* +p+0+0 ++0+ 0 +f40^N0 0 (  0F  ` 0  T  p` 0#  p``" 0 0v:  0  0 0Ph"` P <GOAL 2`2  0 0p`  0 0ll 92 2   0 6@pp U!INTERIOR ANGLES OF QUADRILATERALS" 2" @  g0# pEo,$D 0N   0 h0   0N   0 i0   0n j0 0"`> 0n2 k0 0"` 00n2 l0 0"` 0 m0 0Duk  A EXAMPLE 4 2 Z n0 C *Aj0311784@ F l& 0 l& 0 0 zD(l & ;6.1(2( 0 0<~ @Polygons 2  D( 0  fP o?"6@`NNN?N>xD ,$D 0 JThe sum of the measures of the interior angles of a quadrilateral is 360.$K 2H"l `  0 ` ,$D06 0  f܆33o?"6@ NNN?N` Z"INTERIOR ANGLES OF A QUADRILATERAL#(2# 0 # l o?"6@ NNN?N` l  @ 0  n ,$D0B 0B # lDo?"0@NNN?N 0 B 0 # lDo?"0@NNN?N @B 0 # lDo?"0@NNN?N0  B 0B # lDo?"0@NNN?N @ 0  0e0e    BLCDEF o 8c8c     ?1 d0u0@Ty2 NP'p<'pA)BCD|E||L@ "0e@     @ABC DEEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abN E5%  N E5%  N F   5%    !"?N@ABC DEFFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `ab n ,$@ 0 0  f| o?"6@ NNN?N `p,$0 Since the sum of the measures of each triangle is 180, the sum of the measures of the interior angles of the quadrilateral is 360.$ 25P"H 0 0!޽h ? 33XP___PPT100.]R+D' = @B D' = @BA?%,( < +O%,( < +D' =%(D' =%(DI' =4@BB5BB%(D' =1:Bvisible*o3>+B#style.visibility<*0%(D' =+4 8?RCBBCB#ppt_wB*Y3>B ppt_w<*0D' =+4 8?RCBBCB#ppt_hB*Y3>B ppt_h<*0D' =-g6B fade*<3<*0D' =%(D' =%(D7' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*0K%(D' =-s6Bwipe(left)*<3<*0KD' =%(D' =%(DI' =4@BB5BB%(D' =1:Bvisible*o3>+B#style.visibility<*0%(D' =+4 8?RCBBCB#ppt_wB*Y3>B ppt_w<*0D' =+4 8?RCBBCB#ppt_hB*Y3>B ppt_h<*0D' =-g6B fade*<3<*0D'' =%(D' =%(D7' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*0%(D' =-s6Bwipe(down)*<3<*0D8' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*0%(D' =-g6B fade*<3<*0D' =%(DF' =%(D' =4@BBBB%()))D' =1:Bvisible*o3>+B#style.visibility<*g0%(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>B ppt_x<*g0D' =+4 8?dCB0-#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<*g0+8+0+00 +) 0^N0 !!@P (  ~  s * `   `  c $A ??P  8  P` P r  # l o?"6@ NNN?N0 @   0e0e    BoCDEF A@  Ao 8c8c     ?1 d0u0@Ty2 NP'p<'pA)BCD|E|| ?Q6cMi{o@  s " 0e@        @ABC DEEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abN E5%  N E5%  N F   5%    !"?N@ABC DEFFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `ab P    0e0e    BoCDEF @  o 8c8c     ?1 d0u0@Ty2 NP'p<'pA)BCD|E|| ?Q6cMi{o@  s " 0e@        @ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abN 5%  N 5%  N    5%    !"?N@ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abA@!   f螣 o?"6@ NNN?N  E55&(2""   f o?"6@ NNN?N 0 Fx((2""   f4 o?"6@ NNN?N Fx((2"   f o?"6@ NNN?N   7E(2   fp o?"6@ NNN?NpP 7F(2   fԳ o?"6@ NNN?NP`p 7G(2   f0 o?"6@ NNN?N Pp 7H(2s   ff  o?"6@ NNN?N5 ,$ 0 kSince we know that the sum of the measures of the angles of a quadrilateral is 360, and angles E and G are congruent, we can write the following equation: x + x + 55 + 55 = 360 2(2R"59l p   p  ,$D 0h  c $A ?? `  M   fx8  o?"6@ NNN?Np   q'Solving the equation gives x = 125, so .((2 H  0޽h ? 33}u___PPT10U.avm+1`D' _= @B D' = @BA?%,( < +O%,( < +D' =%(D' =%(DD' =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<*+8+0+0 +; 0^N0 z<@(  <x < c $L `   8   < B <  f o?"6@ NNN?N  fIs quadrilateral JKLM regular?, 2 h < c $A ??    8 p  <P r <  f o?"6@ NNN?Np ! <  f\ƣ o?"6@ NNN?N  E80&(2"" <  f4ˣ o?"6@ NNN?N   Fx((2"" <  fϣ o?"6@ NNN?N  Fx((2"; <  fԣ o?"6@ NNN?N  _ (x - 20): 2"B <  fDo?"0@NNN?N  ` B <  fDo?"0@NNN?N@ @ PB < # lDo?"0@NNN?NP0`B < # lDo?"0@NNN?N `  <  fۣ o?"6@ NNN?Np P  7J(2 <  fdߣ o?"6@ NNN?N@  7K(2 <  f\ o?"6@ NNN?N   7L(2 <  f0 o?"6@ NNN?N   7M(2 < c $A ?? <DP 8 $D 0H < 0޽h ? 33IA___PPT10!.av+$hdD' _= @B D' = @BA?%,( < +O%,( < +D' =%(D' =%(D7' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*<%(D' =-s6Bwipe(left)*<3<*<+  0 d(  dX d C \    d S  \ 0    H d 0޽h ? 3380___PPT10.J@P  0 x(  xX x C \    x S  \ 0    H x 0޽h ? 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