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to continue or press HELPkDefinition of straight anglePress RETURN to continue or press HELPlDefinition of reflex anglePress RETURN to continue or press HELPm>?Test of anglen$U$3/$U* " yes "*@$U*" YES "*K$UyesZ$Uyes" "*i$U*" yes"x$U*" YES"$U*" Y"$U*" Y "*$U*" y"$Uy" "*$Uy$U*" y "*Ա^#GA%_aReview of angleoTest of anglep$U$3, $U*" 4 "*9 $U*" 4"F $U4" "*O $U4Z $U4 )h $Ureflexz $U*" reflex" $U*" REFLEX" $U*" REFLEX "* $Ureflex" "* $U*" reflex "*$U1$Uacute%$U2%$Uright1$U3 1$Uobtuse=^#GA%G_fdG_gdG_hdG_cdReview of obtuse angleqTest of anglep$U$3,$U*" 4 "*9$U*" 4"F$U4" "*O$U4Z$U4 )h$Ureflexz$U*" reflex"$U*" REFLEX"$U*" REFLEX "*$Ureflex" "*$U*" reflex "*ֱ^#GA%_eReview of anglerExample of acute anglesExample of right angletExample of obtuse angleuTest of angleUse cursor control keys or mousev??$U$3GJJW^#GA%a_jkReview of anglePress RETURN to continue or press HELPwv$U$3J&^#GA%-_lPress RETURN to continue or press HELPReview of anglexTest of angley$U$3-$U* " c "*<$U*" C "*I$U*" C"V$U*" c"c$Uc" "*l$Ucw$Uc )$Uc )" "*$U*" c )"$U*" c ) "*$U*" C )"$U*" C ) "*ֱ^#GA%_noReview of anglezy$U$3$U* " c "*+$U*" c":$U*" C "*G$U*" C"T$Uc" "*]$Uch$Uc )w$Uc )" "*$U*" c )"$U*" c ) "*$U*" C )"$U*" C ) "*DZ^#GA%_pReview of angle{=$U.DEF.*.cong.(@$U.EX.*.cong.<C$U.REV.*.cong.xuw$U$1.it.$1 congruent-.$U* next *.GO. .xfm.rCongruencetxyz{~.5#GC%>#GC%0Press RETURN to continue or press HELPvyz{Press RETURN to continue or press HELPxyz{Definition of congruencePress RETURN to continue or press HELP|Example of congruence}Example of congruence~Example of congruence?>Test of congruence""$U$33$U* " 4 " *?$U*" 4L$U4" "*U$U4h$U* " four "*z$U*" FOUR "*$Ufour$U*" FOUR"$U*" four"$Ufour " "*ű}#GC%|Review of congruence$U$3$U* " 4 " *+$U*" 48$U4" "*A$U4T$U* " four "*f$U*" FOUR "*v$U*" FOUR"$U*" four"$Ufour " "*}#GC%|Review of congruence=$U.DEF.*.sim.'@$U.REV.*.sim.9:$U.EX.*.sim.$U$1.it.$1 similarity./$U* next *.GO. .xfm.Similarity")#GC%>#GC%Press RETURN to continue or press HELPDefinition of similarityPress RETURN to continue or press HELP>Test of congruence""$U$3+=$U1:=$UsimilarH#GC%?Review of similarity$U$3)$U1&)$Usimilar4#GC%Review of similarityTest of congruence""$U$33f$U*" "3" "*@f$U*" 3"Mf$U3" "*Vf$U3cf$Uthreeq#GC%Review of similarity:$U.DEF.*.xfm.&=$U.EX.*.xfm.9@$U.REV.*.xfm."$U$1.it.$1 transformation23$U* next *Transformation1Press RETURN to continue or press HELPıIntroduction to transformationsDefinition of transformationPress RETURN to continue or press HELPExample of transformationPress RETURN to continue or press HELP:$U.DEF.*.xlt.&=$U.EX.*.xlt.9@$U.REV.*.xlt.$U$1.it.$1 translation/0$U* next *Translations*1#GT%>#GT%Press RETURN to continue or press HELPPress RETURN to continue or press HELPDefinition and example of translationPress RETURN to continue or press HELPExample of translationExample of translationTest of transformation&&$U$39$U* " yes " *J$U*" YES "*X$U*" YESf$U*" yesu$U*" Y "*$U*" y " *$U*" Y$U*" y$Uyes" "*$Uy" "*$Uyes$Uy۱#GT%Review of translation>?Test of transformation&&$U$39$U* " yes " *J$U*" YES "*X$U*" YESf$U*" yesu$U*" Y "*$U*" y " *$U*" Y$U*" y$Uyes" "*$Uy" "*$Uyes$Uy۱#GT%Review of translation:$U.DEF.*.rot.&=$U.EX.*.rot.9@$U.REV.*.rot.$U$1.it.$1 rotation,-$U* next *Rotation&-#GT%>#GT%Press RETURN to continue or press HELPPress RETURN to continue or press HELPDefinition of rotationPress RETURN to continue or press HELPExample of rotationExample of rotationTest of transformation&&$U$3/$Un9$UnoJ$U* " no "*Z$U*" NO "*g$U*" NOt$U*" no$Uno" "*$U*" N "*$U*" n "*$U*" N"$U*" n"$Un" "*ձ#GT%Review of rotation>?:$U.DEF.*.rfl.&=$U.EX.*.rfl.9@$U.REV.*.rfl.$U$1.it.$1 reflection./$U* next *Reflection%,#GT%>#GT%Press RETURN to continue or press HELPPress RETURN to continue or press HELPDefinition of reflectionPress RETURN to continue or press HELPExample of reflectionTest of transformation&&$U$3/Y$Ua<Y$Ua" "*IY$U*" A"VY$U*" a"d#GT%Review of reflection>?$U$3A$Ua$A$Ua" "*1A$U*" A">A$U*" a"L#GT%Review of reflection:$U.DEF.*.dil.&=$U.EX.*.dil.9@$U.REV.*.dil.űƱ$U$1.it.$1 dilation,-$U* next *DilationűƱ#*#GT%>#GT%Press RETURN to continue or press HELPűƱDefinition of dilationPress RETURN to continue or press HELPExample of dilationPress RETURN to continue or press HELPTest of dilation $U$3)6$Ub36$Ub)A#GT%ȱ?Review of dilation>Review of dilationTest of dilation $U$33$U*" "a d" "*B$U*" "a dQ$Ua d" "*\$Ua dg$Ua,dr$Ud,a}$Ud a$Ud a" "*$U*" "d a$U*" "d a" "*$U* a and d *$Ua$Ud$Ua" "*$Ud" "*#GT%ͱȱ˱Test of dilation $U$33$U*" "a d" "*B$U*" "a dQ$Ua d" "*\$Ua dg$Ud ar$Ua,d}$Ud,a$Ud a" "*$U*" "d a$U*" "d a" "*$U* a and d *ϱ#GT%ȱReview of dilation:$U.DEF.*.sym.&=$U.EX.*.sym.9@$U.REV.*.sym.ڱԱ$U$1.it.$1 symmetry,-$U* next *Symmetryٱڱ۱ܱݱ,3#GT%>#GT%#GT%>#GT%Press RETURN to continue or press HELPPress RETURN to continue or press HELPڱReview of transformationIntroduction to symmetryIntroduction to symmetryDefinition of symmetryPress RETURN to continue or press HELPExample of symmetryExample of symmetryExample of symmetryTest of symmetry $U$3)$U16$U*" "1C$U1" "*N$U1 )^$U*" 1) "*n$U* rotat*w$U3$U*" "3$U3" "*$U*" 3 "*$U3 )$U*" 3) "*$Udilation#GT%߱Review of symmetry$U$3$U1$$U*" "11$U1" "*<$U1 )L$U*" 1) "*[$U*" "1 )j$U1 )" "*z$U* rotat*#GT%>?Review of dilationReview of symmetryTransformation '#GT%>#GT%DẔ$U$1.it.$1 exam()$U* next *.GO. .pln.Final exam#2Press RETURN to continue or press HELP5_$U1F_$Uinformal*Oj$U2^j$Uformal*#FG%#FG%#GE%$U$3h$U4-h$U*" 4 "*;h$U 4" "*Hh$U*" "4Sh$U4 )eh$U* psychoa*#GE%{#FG%>!#FG%>"$U$3R$U1%R$U 1" "*4R$U*" " 1 ?R$U1 )OR$U* lengt*i#GE%e|#FG%>!v|#FG%>"$U$3`$U2&`$U*" 2 "*4`$U 2" "*B`$U*" "2 M`$U2 )]`$U* area *w#GE%s#FG%>!#FG%>"$U$3a$U3&a$U*" 3 "*4a$U 3" "*Ca$U*" " 3 Na$U3 )^a$U* volum*x#GE%t#FG%>!#FG%>"$U$3a$U2&a$U*" 2 "*4a$U 2" "*Ca$U*" " 2 Na$U2 )^a$U* simil*x#GE%t#FG%>!#FG%>"$U$3$Ub&$U*" b "*4$U b" "*C$U*" " b N$Ub )\$U 1//4 p$U*" "1//4" "*$U1//4" "*$U*" "1//4 #GE%#FG%>!#FG%>"$U$3n$U2&n$U*" 2 "*5n$U*" B "*Cn$U 2" "*Qn$U*" "2 \n$U2 )kn$U* 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shape*vy$U*shape*size*#GE%#FG%>!#FG%>"$U$3u$U* false*'u$Uf6u$U*" f "*Eu$U*" F "*Ru$Uf" "*_u$U*" "fiu$Unoru$Un#GE%#FG%>!#FG%>"$U$3!$U* simil*8#GE%4K#FG%>!EK#FG%>"$U$3$Uyes*$U*" yes "*;$U*" Yes "*L$U*" YES "*[$U*" "yesj$Uyes" "*s$Uy$U*" y "*$U*" Y "*$U y " "*$U*" " y $U* congr*#GE%#FG%>!#FG%>"$U$3d$U 3 (d$U*" 3 "*6d$U 3" "*Dd$U*" "3 Qd$U 3 ) ad$U* rotat*{#GE%w#FG%>!#FG%>"$U$3O$U1$O$U1" "*1O$U*" "1<O$U1 )LO$U* trans*f#GE%by#FG%>!sy#FG%>"$U$3 $U2 and 4( $U2,43 $U2 4K $U* reflec* dilat*c $U* dilat* reflec*q$U 2" "*$U*" " 2 $U*" 2 " *$U*refle*! $U*" 4 "* $U 4" "* $U*" "4 $U4) $U*dilat* $U*refle*b* $U*b*refle*!#GE%4#FG%>!.4#FG%>"$U$3$Uno($U*" no "*8$U*" No "*H$U*" NO "*V$U*" "nod$Uno" "*m$Un|$U*" n "*$U*" n "*$U n " "*$U*" " n #GE%#FG%>!#FG%>"$U$3b$U 3 (b$U*" 3 "*5b$U3" "*Bb$U*" "3Ob$U 3 ) _b$U* dilat*y#GE%u#FG%>!#FG%>"$U$3a$U 5 (a$U*" 5 "*6a$U 5" "*Ca$U*" "5Pa$U 5 ) ^a$U* non*x#GE%t#FG%>!#FG%>" >?Congratulations on finishing the exam!GEOMETRY VOLUME 1Answer this question, and press RETURNPress RETURN to continue or press HELP*v****#GE#GP#PS#GA#GC#GS#GT#FG9Iqд  )&Press RETURN to continue or press HELP*Press RETURN for DESKTOPPress RETURN to continue or press HELPReviewPress RETURN to continue, Review?SwBasic Geometrical Notation Disk 2Press RETURN to continue or press HELP]l#GP%>iz#GP%>$5mastery$5needs work$5incomplete#PS%>#PS%>$7mastery$7needs work$7incomplete#GA%> #GA%>$3mastery)$3needs work)$3incomplete5D#GC%>AR#GC%>c$4masteryq$4needs workq$4incomplete}#GT%>#GT%>$6mastery$6needs work$6incomplete$3*The metric unit, and its3abbreviation, referred to<in this course is:LcentimetercmYou must always use thecorrect units in answeringZRemember:cThere is no period afterlthe abbreviated metric unit.questions.@PLANE@POSTULATE@ANGLE@CONGRUENCE @TRANSFORMATION@FINAL EXAMPoints that are NOT on the(same line are said to be8noncollinear.HConversely, points whichXARE on the same line arehcollinear points. A PLANE, like a point and a line, cannot be defined. However, we can say that a plane: 0* Is a flat surface A PLANE, like a point and a line, cannot be defined. However, we can say that a plane: 0* Is a flat surface; ?* Can be tilted A PLANE, like a point and a line, cannot be defined. However, we can say that a plane: 0* Is a flat surface; ?* Can be tilted M* Has position in space A PLANE, like a point and a line, cannot be defined. However, we can say that a plane: 0* Is a flat surface; ?* Can be tilted M* Has position in space [* Goes on forever in all ddirections A PLANE, like a point and a line, cannot be defined. However, we can say that a plane: 0* Is a flat surface; ?* Can be tilted M* Has position in space [* Goes on forever in all ddirections p* Does not have thickness"Planes are4surfaces. Butitis=understoodthatFthey extendforeverO in every Odirection.+represented as flatA plane must contain atleast three NONCOLLINEAR"points.Points that are in the same plane are called COPLANAR POINTS.(If you think of the glassesHas points, then they are coplanar.8on the surface of the tablePoints that are not in the same plane are called NONCOPLANAR(POINTS.pTheseglasses are noncoplanar. Which set of points is noncollinear?01) {E,F}@2) {H,G}P3) {D,H,E}`4) {B,F,H,D}    Remember:0Points on the same line are9collinear.IPoints not on the same lineRare noncollinear.p\$3(The answer is13) {D,H,E} because:a line cannotCbe drawn throughLpoints D, H, and E.p\$3  Which set of points is coplanar?01) {A,D,E,F}@2) {A,D,H,E}P3) {E,D,G,H}`4) {E,F,G}  Remember:0Coplanar points lie in the 9same plane.INoncoplanar points lie in Rdifferent planes.p\$30The answer is 94) {E,F,G}Bbecause pointsKE, F, and G lieTin the same plane.p\$3  Which set of points is noncoplanar? 11) {A,B,E,F}A2) {E,F,G}Q3) {C,E,D}a4) {A,B,C,D}  Remember:0Coplanar points lie in the same9plane.INoncoplanar points lie in Rdifferent planes.p\$3(The answer is11) {A,B,E,F}:because theseCpoints do notLlie in the sameUplane.u\$3 0Is the surface of the eartha plane? -From the surface of6the earth the world?seems flat. But theHearth is round. ItQis not a plane.p\$38What is the smallest numberAof noncollinear points thatJcan be contained in a plane?(Remember:8Any plane contains atAleast three noncollinearJpoints.r\$38How many planesAare there inJthis figure?(Remember:8A plane is a flat surfaceAthat extends indefinitelyJin all directions.p\$38There are 3 planesBin this figure.p\$3 How many plane surfaces does)this figure contain?2(They are not all visible.) How many planes does this)figure contain? There are 6 planes. 8top and bottomhtwo sidespfront and back(\$3 *Some things in geometryare simply assumed.(They are not proved. *Some things in geometryare simply assumed.(They are not proved. <*These assumptions areFcalled POSTULATES.*Postulates describehowpoints, lines, andplanes are related toeach other.* Postulates describehowpoints, lines, andplanes are related toeach other.@*Postulates are usedHtoreach conclusions through deductive reasoning.* Postulates describehowpoints, lines, andplanes are related toeach other.@* Postulates are usedHtoreach conclusions through deductive reasoning.h j*These conclusions arercalled theorems. Given any two points, !there is exactly one *linecontaining them. Any line contains at !least two points.Given any three noncollinearpoints, there is exactly one"plane containing them. Given any three points, there is at LEAST one "plane containing them.Any plane contains at least'three noncollinear points.[If two points lie in a plane,dthen the line containing themmis in the plane.5If two planes>intersect, thenGtheir intersectionPis a line. $Can a line be determined by one point?(A line cannot be determined1by one point.AIt takes two points toJdefine a line.p\$3Can the points in this figure determine a plane?Can the points in this figure determine a plane?  `Yes,three noncollinear points determine exactly one plane. r\$3An ANGLE is the figureformed by two rays"that meet at a common+vertex.GrayYrayavertex Angles are measured in units called DEGREES.)A degree is the amount of sweep of2one of the angle's rays.Zdegrees Angles are measuredin units calledDEGREES.)A degree is the amount of sweep of2one of the angle's rays.BThe symbol for degree is .ZdegreesA complete sweep of a ray of an angle measures 36Odegrees.  Angles are classified according to their measure.! An ACUTE ANGLE has a measure of less than 9O degrees.09O degrees`Acute angle" A RIGHT ANGLE has a measure of exactly 9O degrees.89O# A RIGHT ANGLE has a measure of exactly 9O degrees.89O `This symbol indicates that the angle is a right angle.^#Two lines that intersectto form a right angle are calledPERPENDICULAR LINES.$ An OBTUSE ANGLEhasa measure of morethan 9Odegrees andless# #than 18O degrees.% A straight angle has a $measure of exactly 18O -degrees.&PA REFLEX ANGLE has ameasureYgreater than18O degreesandbless bthan 36O degrees. (18O 36O' 5Can a four-sided figure >contain a reflex angle?This is an exampleof howa four-sidedfigurecan'contain'a reflex angle.p\$3( An angle is divided into2What was the original angle?)two equal obtuse angles. S2) A right angle e4) A reflex angle J1) An acute angle \3) An obtuse anglep\$3An OBTUSE ANGLE has a measure%ofmore than 9O degrees and.lessthan18O degrees.% Dividing a reflexangle 'in half willresult in 0two obtuse0angles.p\$3) The angles formed by dividing an acute angle in two are both between O and 45 degrees.*Dividing a right angle in halfresults in exactly two 45 degree"angles.+The angles formed bydividingan obtuseangle in two are"between 45 and 9Odegrees.,Move the colored line!over the end point of*one of the other lines3to form a right angle.-Remember:The sides of a right angle are!perpendicular to each other.aThat is, a right angle measuresj9O degrees.#Watch the colored!line move to form*a right angle..Which of these is a straightangle? Ya) b)c)d)/:of18O degrees.A straight angle forms a!straightline.1That is,it has a measurep\$3&A straight angle measures"18O degrees.Xa)b)c)d)hOnly figure c) is astraight angle.p\$30 (CONGRUENT FIGURES have:8*The same size and@shapeP*Equal measures of Xcorresponding parts1These pairs of figures are congruent.2Congruent figures are like clones.They are identical to each other.hBut they may have differentqpositions and directions.3Figures that have(* Different sizes4(* Different sizes@orFigures that haveX* Different shapes5hare not congruent.X* Different shapes(* Different sizes@orFigures that have5 `How many figures in A iarecongruent to B?6Congruent figures do not have!to point in the same direction.aThey may even overlap.q\$37`There are four figures in Aithatare congruent to B.q\$38(SIMILAR FIGURES have8* The same shapeH* Butnot necessarilyPthe same size9Notice that similar figuresneed have only the same SHAPE.:Notice that similar figures need have only the same SHAPE.pBut congruent figures must have the same size AND shape.;HThese two figures are:X1) similar3) concurrenth2) congruent 4) equal<8Congruent figures must haveHBOTH the same SIZE and SHAPE.p\$3The figures are similar because theyhave the same shape.p\$3=Squares of different sizes are similar. How many squares can you find in this figure?813H33p13`11>There are three similar squares shown in this figure. 3833 1X13L11p\$3? Congruence and similarity relate figures by size and shape. @These can be used to discuss how figures are changed or "transformed" into new figures. * A TRANSFORMATION is,a process in which8thesize,8direction,Dorposition of aPfigureis changed to\forma new figure.YYou are going to study fourbkinds of transformations.@A transformation that changes afigure by moving all of its parts"the same distance in the same+direction is called a TRANSLATION.AThis person is going from position A to position B.8She is moving along aline from one position to another.XThis is an example of translation.BA translated figure is congruenttothe original figure.CXHas this figure been translated?D(The figure has been translated4because all of its parts have@been moved the same distanceLin the same direction.p\$3Does a line segment have the same length after being translated?E(After translation, the new figure is4congruent to the original figure.@It maintains the same size and shapeLas it moves.p\$3 One type of)transformation2isROTATION.Dpart of a figureMturns in unisonVaround a point.;In rotation, eachF The axe is being rotated about point P.GA rotated figure is'congruent to the0original figure.HHas this figure been rotated?I A figure has NOT been rotated if it has not been turned about a point.hIt has been translated.p\$3AA REFLECTION changes a figurebyflipping it over a line at"anequaldistance from that line.JThe reflected figure is congruent0That is, it has the same size and'to the original.9shape.KChoose the pair of figures that illustrates reflection.Lp\$3A reflection changes a!figure by flipping it*over a line at an equal3distancefrom that line.KOnlyfigure A illustrates reflection because the figure has been changed byflipping it over a line at an equaldistance from the line.p\$3M A transformation)that changes a 2figure by making ;it larger orDsmaller iscalledMa DILATION.eA dilated figurerechanges neithenits shape nor nits position.N(Watch the iris of1the eye dilate:when the flashlightCis turned on.OhChoose the figure that doesqNOT illustrate dilation. Xa)b)c)PThe middle figure is NOT an exampleof dilation because the circles have(not been made larger or smaller.p\$3Q8Dilation changes a figure byDmaking it larger or smallerPwithout any rotation.(Remember:p\$3 Which two figures)below are dilations2of this one?R(Your answer is partly correct.@There is another figure thatIis also a dilation of the Rgiven one.p\$3 PBoth figures A) and D) Yaredilations of the babove figure.p\$3SYou have seen four kindsoftransformations:41) TranslationAYou have seen four kindsoftransformations:42) RotationFYou have seen four kindsoftransformations:43) ReflectionKYou have seen four kindsoftransformations:44) DilationO If one or more )transformations change 2a figure so that it ; APPEARS not tochange D at all, thenthefigure M has a specialproperty V called symmetry. Watch the square.XEven though the square has been rotated, it still looks the same.TWatch the figure below.PNotice that rotation HAS\CHANGED the position ofhthe figure.U(A figure has SYMMETRY1if it can be changed:by a transformationCso that it appearsLnot to have changedUat all.The transformation can be: (* Rotation 8* Reflection H* Translation[Figures can have symmetry by onedor more of these transformations.PThis flower has symmetry because[certain rotations will not appearfto change it.VA butterfly has symmetry byreflection along the line of&itsbody.WThis wave pattern has symmetry by#translation, since it can be moved.over to the right and it does not9appear to have moved through space.X0Does this figure have symmetry by: @1) Rotation P2) Translation `3) DilationY0If a figure does notchange9 aftera certaintransformation,@then@that figure is symmetricalI to that Iparticular transformation.n\$39A figure which has beenBdilated changes its size.p\$3h\$3PThis figure has symmetry by rotation.ZYou have completed Disk 2.0If you wish you can review the material covered by typing "review all" or continue and take either an informal or formal final exam. The final exam includes twenty five questions. To choose an exam, @type @X@1@X@ for informalHF-GH(with feedback) `type `X`2`X` for formal.hF-GXR-T8R-T@FORMAL EXAM[ @INFORMAL EXAM[In which of these activities would geometry NOT be useful?  01) Textile DesignP3) Construction@2) Navigation`4) Psychoanalysisp5) Art&18Geometry would not be useful Din psychoanalysis.p\$3 You see an aquarium in a shop and make several measurements to check that it meets your needs.,Answer the following question:<You measure a side and find it to be 12 inches.TYou have measured:\1) Length 2) Area 3) Volume 4) Angle&2You have measured length.p\$3\ You see an aquarium in a shop and make several measurements to check that it meets your needs.,Answer the following question:<You want to buy a glass top for it and find that you need two square feet of glass.\You have measured: 1) Length 3) Volumet2) Area 4) Angle&3 You have measured area.p\$3]You see an aquarium in a shop4 and make several measurements to check that it meets your needs.(Answer the following question:8You want to fill it with sand to a depth of three inches and find you need half a cubic foot of sand.XYou have measured:h1) Length3) Volumex2) Area 4) Angle You have measured volume.p\$3^You see an aquarium in a shop and make several measurements to check that it meets your needs.&Answer the following question:6You find it too small for your needs and decide to buy one that is the same shape but twice as large.^The two aquariums are:v2) Similar4) None of thesen1) Congruent 3) Symmetric&5The two aquariums are similar$because they have the same shape.p\$3_ What is the area of a square whose sides are each 1/2 cm long? @a) two square cm  Pb) 1/4 square cm  `c) one square cm  pd) 1/2 square cm &6 (Area = length of side x0length of side@1/2Area = 1/2 cm x 1/2 cm PArea = 1/4 square cmX1/2p\$3`You measure a wall to determine!if it is perpendicular to the*floor. You are measuring::1) Volume J2) AngleZ3) Areaj4) Perimeter &7(You are measuring8the angle of theHwall to the floor.p\$3aWhich of these figures is a ray?&8bFigure c is a ray:p\$3ca)b)98Which of these figures representsPc)d)Ha plane?d9A plane is a FLAT surface that0The answer is figure d.Bextends indefinitely in ALL Kdirections.p\$38What is the least number ofApoints contained in a plane?%1O8The answer is three points.@(See postulate on plane)p\$3Which set of points in the figure below is collinear?61) {A,B,C}F2) {A,D,C}V3) {C,F,D}f4) {C,F,E}%11e0The answer is set 3){C,F,D}<because points C,F, and D Hlie on the same line.p\$3Which set of points in the figure below is coplanar?01) {A,D,F,B}@2) {A,B,D}P3) {A,B,C,D}`4) {A,E,F,B}%12e0The answer is set 2) {A,B,D}<because points A, B, and D Hlie in the same plane.p\$3(Two rays meet at a common endpoint.8They determine:H1) a lineT2) an angle`3) anarcl4) a half plane%13 The two rays determinean angle.p\$3fAn angle whose measure is more(than 9Oand less than 18O is:81) ReflexH2) ObtuseX3) Acuteh4) Right%14 @The angle is obtuse.p\$3An angle whose measure is less(than 9O is:81) ObtuseH2) RightX3) Reflexh4) Acute%15 @The angle is acute.p\$3 Congruent figures have the same:01) size@2) shapeP3) size and shape`4) direction%168Congruent figures haveDthe same size and shape.p\$3HSimilar figures must have theTsame size.%17( Answer TRUE or FALSE(False8Similarfiguresdo NOT need to have Dthe same size.OBut they must have the same shape.p\$3Are these figures similar or$congruent?%18g The figures are similar ,because they have the8same shape. DThey are not congruentPbecause they have different\sizes.p\$30Two figures are congruent to a <third figure.HAre they congruent to each other?%198Two figures that are congruent to aDthird figure must be congruent toPeach other.(Yes.p\$3You are in an amusement park and decide to take some rides.0Answer the following question:@You take a ride on the merry-go- round. What transformation describes your movement?`1) translation3) rotationp2) reflection4) dilation%2O@(The merry-go-round rotates Laround its center.) 4your movement. (Rotation describesp\$3You are in an amusement park and decide to take some rides.0Answer the following question:@You go down the water slide into a pool. What transformation describes your movement?`1) translation3) rotationp2) reflection4) dilation%218All the parts of your body moveCdown the slide the same distance Pin the same direction.,movement. Translation describes yourp\$3You are in an amusement park and decide to take some rides.(Answer the following question:8You enter the hall of mirrors and see a ten foot enlargement of yourself. What combination of twoXyousee?h1) translation3) rotationPtransformations describes whatx2) reflection 4) dilation%22(Both reflection and dilation describe0 4what you see.@Your image is reflected in theLmirror and is also enlargedXby the curvature of the glass.p\$38Is a dilated figure congruent to Dthe original figure?%230Congruent figures have the same No, it is not.<size and shape.HA dilated figure is either largerTor smaller than the original one.p\$3(Under which transformation is3the new figure NOT congruent ?to the original?W1) translation3) dilationg2) reflection4) rotation%24 Only under dilation is the new+figure not congruent to the6original, because dilationAincreases or decreases the LSIZE of the figure.p\$3 Under which transformation is,the new figure NOT similar to8the original:H1) translation4) rotationX2)reflection5) none ofh3) dilation`the above% 25(The answer is 5) none of the above. 4Under none of the four@transformations is the shapeLof the new figure differentXfrom that of the original.p\$30Your score:H\#GE percenthUSE THESE WORDS TO:*Go to another concept:goto, show me, teach(*Review a concept:0review, review all@*Test your progress:Hexam, testX*Ask questions:define,`example, what isp*Other commands:score, overview,xagain, quit, resume, restarti@THE ENDj OVERVIEW Disk 2 Here is what you will learn onthis disk:0PLANEOPOSTULATES:*Coplanar pointsD*NoncoplanarpointsZ* Postulates on lined* Postulates on planex(cont'd)(ANGLE 2* Degrees<* Acute angleF* Right angleP* PerpendicularlinesZ* Obtuse angled* Straight anglen*Reflex anglex(cont'd) OVERVIEW (cont'd)Disk 2 OVERVIEW(cont'd)Disk 2 CONGRUENCE **Similarity4TRANSFORMATION>* TranslationH* RotationR* Reflection\* Dilationf* SymmetrysFINAL EXAM8Plane \$5Basic Geometrical Notation_!(Disk 2APostulate\$7JAngle \$3SCORESCongruence\$4\Transformation\$6 oFinal Exam\#GEpercentkA PROTRACTOR is an instrument used to measure angles.hIts curved edge contains a scale marked in degrees.l To measure this angle, place the protractor over both arms."  m To measure this angle, place the protractor over both arms.Notice that the protractor is placed over  one arm of `the angle, and the protractor's center is placed over the meeting point of the angle's arms.n  This angle's measure ishRead the angle measure off the scale on the protractor. 55 degrees.ol|88||8xx8||8|<<`<|fl0fF8l8pvp88pf< 80 0 ~~`0 0```nff>fff~fff<<f<flxpxlf`~fv~~nfff<ff<f>``|fff|<```<>fff>ff>|``|f8<p``flxlf8<|ffff>|f```>`<|~f>fff<|lf<|~ 0~0p p` 44b~l|88||8xx8||8|<<`<|fl0fF8l8pvp88pf< 80 0 ~~`0 0```nff>fff~fff<<f<flxpxlf`~fv~~nfff<ff<f>``|fff|<```<>fff>ff>|``|f8<p``flxlf8<|ffff>|f```>`<|~f>fff<|lf<|~ 0~0p p` 44b~ 0HH0~$ff~f&$,4$d<<f ~Ù}xc8ll8x~~~ `` 8||8  $ff$<~~< 888llllllll0|x 00f8l8vv``0```0`00`f<`<|fl0fF8l8pvp88pf< 80 0 ~~`0 0```nff>fff~fff<<f<flxpxlf`~fv~~nfff<ff<f>``|fff|<```<>fff>ff>|``|f8<p``flxlf8<|ffff>|f```>`<|~f>fff<|lf<|~ 0~0p p` 44b~stuvw0`1aTA2b}3cbAbvcbAbocbAblcbA` aObgcbA`aJbbcbA`aEb]cbA@xyz{A0`1ayA`aoA`aeA`a[A`aQA`aGA`a=A`a5A`a-2bT3cHUA` a%bTc>UA` a!bTc6UA`abTc.UA`ab Tc(UA`abTc"UAabTc UAabTcUAabTcUAAA@A@|0`A@#}~0`71a72bA@ ~0`71a72bA@~0`<1a72bA@0`2-A@ 0`.'A@ 0`.'1a82b@(3c.E4d*(5e6f7gA@1a2b3c4dA@0`H1a492b2P3c,Aa<,Aa:,Aa8,Aa6,Aa4,Aa2,Aa2.Aa20Aa28Aa2BAa2MAa2ZAa2sAa2A0`AA0`,%1aAAA0`,%AA0`T1aAA0`S1aAA0`BA~0`1a72bA@1aW2b*WA@0`VA@0`A@0`VA@0`A@0`VA@0`A@0`VA0`>A@1a$?2b2?3c*G4d,;5e./6f&77g0CA@`>A`>A`>A` >A` >A`>A`>A`>A`>A`>A`>A`>A`>A`>A` >A@0`D1a=2b@03cW4dH5eE6fK7gWAb>0Ab<0Ab:0Ab80Ab60Ab40Ab20Ab00Ab.0Ab,0Ab*0Ab(0Ab&0Ab$0Ab"0Ab 0Ab0Ab0Ab0Ab0Ab0Ab0Ab0A0`AA@3c$KA@6f WA@4d"FA@2b$;A@5e&RA@1a(DA0`*1a2b3c4d5e6f7gA0`(aAǀ3c01A0`$L1aAA0`$?1a2b">3c,)4d,P5e.16f,MAA~0`71a72b4dGA0`gA@#0`[A@0`UA0`&CA@0`$A@0`2A@0`2A@0A0` JA@ 1a 0A@0` %1abA@0`1a1bA@`1a1bcA@0`<1abcA@0`"1aOA@1a2bOA@ 2b3cOA@ ‚Ã0`*A@0`*1aO2b3c4d5e6f7gA@1A@ɀāłƃ0`-1a(52b3c4d5e6f7gA2bk3c,eAA€ȁɂʃ˄0`$;A@0`?A@0A@̓΄υ0`$gA@0`$UA@0`$MA@0` RA@0`]1a"QA@с҂0`"A@0A@0A@ԁ0` 71a KA@0` 71a K2b3c4d5e6f7gA@1aA@ƀ0`EAց1a$7A؁0`$5A0`A`&BA`(FA`*GA`,GA`.GA    0`,(1a2b3c4d5e6f7g4HA@0`*FacA@0`1a._bcA@`1a8BbcA@`1a2b8%cdefA@`a2b.#cdefA@^ 0`S1a,2b3c4d5e6f7gA@1a5A@ƀ0`"=A@0`1a"A@0`"1aA0`$1a AA`$A`$A`$A`$A`$A`$A` $A`"$A`$$A`&$A`($A`,$A`.$A`0$A`2$A`4$A`6$A`8$A0`;1a2b3c4d5e6f7gA@0`&;aA@À0`?A0`31aAA0`3A0`.5A@0`,%abcA@0`*abcA0`4?1a2b3c4d5e6f7gA@0`49A@ƀ <0`31a AA 0`:A!"#0`>#1aY2bAA"#0`>1a)A$%&'0` (1a2b3c4d5e6f7gA@0`1a$A@1a2b"A@2b3c$A@()*0`/A@1a/A@1a"A@1aAA+,0`1a2b3c4d5e6f7gA0À-0`+A./0`Q2bQ3c*QA@4dQA@dQA@dQA@dQA@dQA@dQA@dQA@d QA@d"QA@d$QA@d&QA@d(QA@d*QA@00`>N1aAA01230`"1a2b3c4d5e6f7gA0` aA0`"aA0`"A0`"A@A@A@450`;1a/2b3c4d5e6f7gA@Ѐ60`=A70`;A890`@A:0`(A;0`0A<0` 1a.AA=0`(7A>?@A0`Ac.HAc.RA3c0WAA2b8"A@`4U2b:J4d8"AA`4TA`4SAAA@2b8"4dA`4UA`4VAAA@A2ALMNOPQR0`>2b>5e4'A@4d0Ad0Ad0Ad0Ad0Ad0Ad0Ad0Ad0A@1a@Aa>Aa< A0`>1a:2b>3c< 4d05e4'6f7gA@3c<$A@ƀSTU0`&11aF12b$VAVWXYZ[\]0`1aF2b 3cB 4d5e6f7gA2b 3cB A2b 3cB A^0`&A^_0`&1a$,A`&A`&A`&A`&A` &A` &A`&A`&A`&A^_0`&1a$,A^_`0`&1a$,2b2A =&####ꪪꪪꪪꪫ꾪ꪫꪫꯪ꾪ꪫꪫ꾪꾪ꪪꪫꪪꯪꪫ꾪###+.++++++$ꪪꪪ꪿ 꾾꾾꾾ꪯ"++'꾾 꾪꾪ꪣꪣ+++++ ;"????򪪯 ?򪪯 ?򪪯?򪪯?򪪯??򪪯????򯪫? 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