-FTTPO1SBDUJDF-FWFM# *À>VÌViÊ ,%33/. 1ÃiÊÌ iÊ`>}À>ÊÌÊ`iV`iÊÜ iÌ iÀÊÌ iÊ}ÛiÊÃÌ>ÌiiÌÊÃÊÌÀÕiÊÀÊv>Ãi° Ê £° 0OINTS ( ) AND ' ARE COLLINEAR TRUE AND &' ARE OPPOSITE RAYS ΰ %' FALSE TRUE AND PLANE *+( IS () Ê x° 4HE INTERSECTION OF %& IS POINT ' () AND *' Ê È° 4HE INTERSECTION OF %& FALSE £° Y X ! NO ÊÓ£° X Y ! YES ÓÓ° X Y ! NO Óΰ X Y ! NO ÊÓ{° X q TRUE Ê Ç° 4HE INTERSECTION OF PLANE %'( AND PLANE *') IS POINT ' Ê£n° Y X ! YES £ä°Ê3AMPLE ANSWER Óx° a X a RAYÊ ÓȰ X a AND X q -iÌV ÊÌ iÊwÊ}ÕÀiÊ`iÃVÀLi`° Ê ° 4WO RAYS THAT DO NOT INTERSECTÊ SEGMENT RAYSÊ Óǰ --" Ê£°£ TRUE n° 4HE INTERSECTION OF PLANE %&) AND PLANE *+' IS (' Óä° Y X ! NO À>« ÊÌ iÊiµÕ>ÌÞÊÊ>ÊÕLiÀÊi°Ê/iÊÜ iÌ iÀÊÌ iÊ}À>« ÊÃÊ>Ê Ãi}iÌ]Ê>ÊÀ>ÞÊÀÊÀ>ÞÃ]Ê>Ê«Ì]ÊÀÊ>Êi° FALSE &OR USE WITH PAGES n 9ÕÊ>ÀiÊ}ÛiÊ>ÊiµÕ>ÌÊvÊ>ÊiÊ>`Ê>ʫ̰Ê1ÃiÊÃÕLÃÌÌÕÌÊÌÊ `iÌiÀiÊÜ iÌ iÀÊÌ iÊ«ÌÊÃÊÊÌ iÊi° TRUE Ê Ó° 0OINTS ( ) AND * ARE COPLANAR ARE COPLANAR Ê {° !LL POINTS ON ') AND '& --" Ê£°£ *À>VÌViÊÊ CONTINUED ,%33/. &OR USE WITH PAGES n {X{ a POINT £ä° 4HREE PLANES THAT INTERSECT IN ONE LINE 3AMPLE ANSWER Ón°Ê>° FOURLEGGED STOOL 0OSSIBLE ÊÓn°Ê #OUNTER 3TOOLS 4WO DIFFERENT TYPES OF STOOLS ARE SHOWN BELOW EXPLANATION 4HE TIPS OF THE LEGS Ê££° 4HREE LINES THAT INTERSECT IN THREE POINTSÊ £Ó° ! RAY THAT INTERSECTS A PLANE IN ONE POINT 3AMPLE ANSWER SIDE TO SIDE ON YOUR KITCHEN mOOR 7HICH OF THE TWO STOOLS COULD THIS POSSIBLY BE %XPLAIN WHY THIS MIGHT OCCUR L° 3UPPOSE THAT EACH STOOL IS PLACED ON A mAT SURFACE THAT IS SLIGHTLY SLOPED $O YOU EXPECT EITHER OF THE STOOLS TO ROCK FROM SIDE TO SIDE %XPLAIN WHY 0OSSIBLE EXPLANATION 4HE THREELEGGED STOOL WILL NOT ROCK BECAUSE THE TIPS OF ITS LEGS WILL ALWAYS BE COPLANAR 4HE FOUR OR WHY NOT LEGGED STOOL MAY ROCK IF THE TIPS OF ITS LEGS ARE NOT COPLANAR ÊÓ°Ê 0ERSPECTIVE $RAWINGS 2ECALL FROM THE TEXT THAT A PERSPECTIVE DRAWING IS DRAWN USING VANISHING POINTS 9ES IT HAS ONE VANISHING POINT Ê >°Ê $OES THE DRAWING AT THE RIGHT REPRESENT A PERSPECTIVE DRAWING %XPLAIN WHY OR WHY NOT L° 5SING HEAVY DASHED LINES DRAW THE HIDDEN LINES OF THE PRISM V° 2EDRAW THE PRISM SO THAT IT USES TWO VANISHING POINTS ÊÝiÀVÃiÃÊ£Îq£x]ÊÕÃiÊÌ iÊ`>}À>° ʣΰ .AME DIFFERENT RAYS Ê£{° .AME PAIRS OF OPPOSITE RAYS Ê£x° .AME LINES THAT INTERSECT AT POINT # "# #" #$ $# %# #% %$ $% £Î° !" "! !# #! £{° 3AMPLE ANSWER !" "! AND #! #" #$ !" £x° %# ] AND !$ 3EE BELOW ʣȰ $RAW FOUR NONCOLLINEAR POINTS ! " # AND $ 4HEN SKETCH !"z "# ʣǰ 3KETCH PLANE - INTERSECTING PLANE . 4HEN SKETCH PLANE / SO THAT IT INTERSECTS PLANE . BUT NOT PLANE - Ê £È° 3AMPLE ANSWER 'EOMETRY #HAPTER 2ESOURCE "OOK 'EOMETRY #HAPTER 2ESOURCE "OOK *À>VÌViÊ ,%33/. Ê CM Ó° Ê £°Ê CM ΰ 1ÃiÊÌ iÊ-i}iÌÊ``ÌÊ*ÃÌÕ>ÌiÊÌÊwÊ`ÊÌ iÊ`V>Ìi`Êi}Ì ° Ê {°Ê &IND 24 x° &IND "# Ê Ê Ê È° &IND -. *ÌÊÌ iÊ}ÛiÊ«ÌÃÊÊ>ÊVÀ`>ÌiÊ«>i°Ê/ iÊ`iÌiÀiÊÜ iÌ iÀÊÌ iÊ iÊÃi}iÌÃÊ>i`Ê>ÀiÊV}ÀÕḭ Ê Ç° ! " # $ Ê ] ] ] ÊÓ£° #9 ÊÓÓ° #$ ÊÓΰ 8# ÊÓ{° #: Ê Ê ° % & ' ( Ê Óǰ &IND .0 +( ÊÎä°Ê (* X *+ X X X (* *+ +( X X Ó° (* ]z ]z X (* *+ *+ X +( *+ X Σ° (* X X X X *+ X (* *+ --" Ê£°Ó Ê ÓȰ &IND !# ÊÓn°Ê (* X X X (* *+ ] 23zAND 45z CONGRUENT ] ] ] %'zAND &(z NOT CONGRUENT *ÌÊÊÃÊLiÌÜiiÊÊ>`ÊÊÊÊʰzÊ1ÃiÊÌ iÊ}ÛiÊvÀ>ÌÊÌÊÜÀÌiÊ>Ê iµÕ>ÌÊÊÌiÀÃÊvÊݰÊ-ÛiÊÌ iÊiµÕ>̰Ê/ iÊwÊ`ÊÊ>`ʰ £ä° 2 3 4 5 ] ÊÓx°Ê &IND 34 Ê ÊÓä° "$ `ÊÌ iÊ`V>Ìi`Êi}Ì °Ê-i}iÌÃÊ>ÀiÊÌÊ`À>ÜÊÌÊÃV>i°® -.zAND /0z NOT CONGRUENT Ê Ê£° !" n° - . / 0 ] !"zAND #$z CONGRUENT Ê &OR USE WITH PAGES n ÊÌ iÊ`>}À>]Ê«ÌÃÊ]Ê]Ê ]Ê>`ÊÊ>ÀiÊVi>À]Ê«ÌÃÊ ]Ê8]Ê9]Ê>`Ê<Ê >ÀiÊVi>À]ÊÊÊ ÊÊ 8ÊÊ9<]ÊÊÊx{]Ê89ÊÊÓÓ]Ê>`Ê8<ÊÊÎΰÊ`Ê Ì iÊ`V>Ìi`Êi}Ì ° CM *À>VÌViÊÊ CONTINUED ,%33/. &OR USE WITH PAGES n i>ÃÕÀiÊÌ iÊi}Ì ÊvÊÌ iÊÃi}iÌÊÌÊÌ iÊi>ÀiÃÌÊÌiÌ ÊvÊ>ÊViÌiÌiÀ° --" Ê£°Ó ARE NOT COPLANAR >°Ê /NE STOOL ROCKS SLIGHTLY FROM Ê 3AMPLE ANSWER +( X ] ÊÎÓ° (IKING /N THE MAP !"zREPRESENTS A TRAIL THAT YOU ARE HIKING 9OU START FROM THE BEGINNING OF THE TRAIL AND HIKE FOR MINUTES AT A RATE OF MILES PER HOUR (OW MUCH FARTHER DO YOU NEED TO HIKE TO REACH THE END OF THE TRAIL MI 1ÃiÊÌ iÊÕLiÀÊiÊÌÊwÊ`ÊÌ iÊ`V>Ìi`Ê`ÃÌ>Vi° Ê ££° !" £Ó° !$ £Î° #$ £{° "$ £x° #% £È° !% £Ç° "% £n° $% $ 'EOMETRY #HAPTER 2ESOURCE "OOK 'EOMETRY #HAPTER 2ESOURCE "OOK *À>VÌViÊ ,%33/. ] Ê £° ,INE 23 BISECTS 01zAT POINT 2 &IND 21 IF 01 CENTIMETERS ] Ê Ó° ,INE *+ BISECTS -.zAT POINT * &IND -. IF *- ]zFEET FT ÊÓä° ] Ê {° 0OINT # BISECTS !"z &IND #" IF !" METERS Ȱ &IND !- ǰ &IND -2 `ÊÌ iÊVÀ`>ÌiÃÊvÊÌ iÊ`«ÌÊvÊÌ iÊÃi}iÌÊÜÌ ÊÌ iÊ }ÛiÊi`«Ìð n° 3 AND 4 | ]z ° , AND 0 £ä° ( AND ) ] £Ó° 2 - £Î° 2 - £Ç° Ê Ê Ê $UNKIRK TO !LLENTOWN MI #LEARlELD TO ,AKE #ITY MI #LEARlELD TO !LLENTOWN MI ,AKE #ITY TO !LLENTOWN MI 'EOMETRY #HAPTER 2ESOURCE "OOK *À>VÌViÊÊ CONTINUED ,%33/. Ó° -/0 0/- OR / / /- /0 ΰ %&' '&% OR & & &% &' &OR USE WITH PAGES n 1ÃiÊ>Ê«ÀÌÀ>VÌÀÊÌÊi>ÃÕÀiÊÌ iÊ>}iÊÌÊÌ iÊi>ÀiÃÌÊ`i}Àii°Ê7ÀÌiÊÌÜÊ >iÃÊvÀÊÌ iÊ>}i°Ê/ iÊ>iÊÌ iÊÛiÀÌiÝÊ>`ÊÌ iÊÃ`iÃÊvÊÌ iÊ>}i°Ê Ê 3EE ABOVE *ÌÊÌ iÊ«ÌÃÊÊ>ÊVÀ`>ÌiÊ«>iÊ>`Ê`À>ÜÊ °Ê >ÃÃvÞÊÌ iÊ>}i°Ê / iÊ}ÛiÊÌ iÊVÀ`>ÌiÃÊvÊ>Ê«ÌÊÌ >ÌÊiÃÊÊÌ iÊÌiÀÀÊvÊÌ iÊ>}i° Ê £° Ê£° ! " # Ó° ΰ x° +-. Ȱ 01- ǰ *-, n° 10. ° 0,+ {° 3AMPLE ANSWER + RIGHT ÊÓ£° ! " # ÓÓ° ! " # OBTUSE 3AMPLE ANSWER ° 3AMPLE ANSWER +,0 OBTUSE ££° 'IVEN M134 lND M132 ÊÓΰ ,ET X REPRESENT THE MEASURE OF AN OBTUSE ANGLE 7HAT ARE THE POSSIBLE VALUES OF X X ÊÓ{°Ê 3 Ê TREETS 4HE DIAGRAM SHOWS THE INTERSECTION OF FOUR STREETS )N THE DIAGRAM M !%" M "%# M#%$ AND !%$ IS A RIGHT ANGLE 7HAT IS THE MEASURE OF #%$ `ÊÌ iÊ`V>Ìi`Ê>}iÊi>ÃÕÀi° RIGHT 3AMPLE ANSWER x° 3AMPLE ANSWER +,- STRAIGHT 1ÃiÊÌ iÊ}ÛiÊvÀ>ÌÊÌÊwÊ`ÊÌ iÊ`V>Ìi`Ê>}iÊi>ÃÕÀi° £ä° 'IVEN M !"# lND M#"$ Ȱ 3AMPLE ANSWER -10 ACUTE ǰ 3AMPLE ANSWER *-+ ACUTE n° 3AMPLE ANSWER 0 ACUTE ACUTE 3AMPLE ANSWER ÛiÊ>Ì iÀÊ>iÊvÀÊÌ iÊ>}iÊÊÌ iÊ`>}À>°Ê/iÊÜ iÌ iÀÊÌ iÊ>}iÊ >««i>ÀÃÊÌÊLiÊ>VÕÌi]ÊLÌÕÃi]ÊÀ} Ì]ÊÀÊÃÌÀ>} ̰ {° *+. Óä° ! " # ACUTE 3AMPLE ANSWER £Ó° Az z z £Î° Bz z £{° Cz z ÊÓx°Ê & Ê LAGS )N THE mAG SHOWN -.0 IS A STRAIGHT £x° Dz z Ê ÊLÃiVÌÃÊ °Ê`Ê ° ÊÌ iÊ`>}À>]ÊÊ Ê Ê£È° 'EOMETRY #HAPTER 2ESOURCE "OOK Ê £n° £Ç° --" Ê£°{ --" Ê£°{ Ê£° !"# #"! OR " " "! "# &OR USE WITH PAGES n Óǰ $UNKIRK TO #LEARlELD MI $UNKIRK TO ,AKE #ITY MI *À>VÌViÊ Ón° $UNKIRK AND !LLENTOWN $UNKIRK AND #LEARlELD 'EOMETRY #HAPTER 2ESOURCE "OOK ,%33/. --" Ê£°Î £° --" Ê£°Î Ê Ê MARATHON 7HICH OF THE FOLLOWING PLANS IS THE BEST ROUTE FOR THE MARATHON %XPLAIN ° $UNKIRK TO #LEARlELD TO !LLENTOWN TO $UNKIRK ° $UNKIRK TO #LEARlELD TO ,AKE #ITY TO !LLENTOWN TO $UNKIRK ° $UNKIRK TO ,AKE #ITY TO #LEARlELD TO $UNKIRK ° $UNKIRK TO ,AKE #ITY TO !LLENTOWN TO $UNKIRK #HOICE # BECAUSE THE TOTAL DISTANCE OF THE PATH IS CLOSEST TO MILES Ê ÊÓ°Ê 4HE MAP IS BEING USED TO PLAN A MILE 7HICH TWO TOWNS ARE FARTHEST APART 3EE BELOW ÊÓn°Ê 7HICH TWO TOWNS ARE CLOSEST TOGETHER Ê£n° 2OUND TO THE NEAREST TENTH OF A MILE 3EE BELOW ÊÓǰ &IND THE DISTANCE BETWEEN EACH PAIR OF TOWNS / iÊVÀ`>ÌiÃÊ>ÀiÊ}ÛiÊÊið £x° 2 - Ê Ê ÊÝiÀVÃiÃÊÓÇqÓ]ÊÕÃiÊÌ iÊ>«°Ê/ iÊV>ÌÃÊvÊÌ iÊÌÜÃÊÊÌ iÊ>«Ê >Ài\ÊÕÀÊä]Êä®]Ê i>ÀwÊi`Ê£ä]ÊÓ®]Ê>iÊ ÌÞÊx]ÊÇ®]Ê>`ÊiÌÜÊ£]Ê{®°Ê `ÊÌ iÊi}Ì ÊvÊÌ iÊÃi}ḭÊ,Õ`ÊÌÊÌ iÊi>ÀiÃÌÊÌiÌ ÊvÊ>ÊÕ̰ ʣȰ 4HE MOVIE THEATER IS HALFWAY BETWEEN YOUR HOUSE AND THE MALL ON THE SAME ROAD >° $RAW AND LABEL A SKETCH TO REPRESENT THIS SITUATION (OW FAR IS YOUR HOUSE FROM THE MOVIE THEATER MI L° 9OU WALK AT AN AVERAGE SPEED OF MILES PER HOUR !BOUT HOW LONG WOULD IT TAKE YOU TO WALK TO THE MOVIE THEATER H 1ÃiÊÌ iÊ}ÛiÊi`«ÌÊ,Ê>`Ê`«ÌÊÊvÊÊ,-ÊzÌÊwÊ`ÊÌ iÊVÀ`>ÌiÃÊvÊ Ì iÊÌ iÀÊi`«Ì° Ê£{° 2 - +,zz z q z -.zz z NOT CONGRUENTÊ /0zz z 12zz z NOT CONGRUENT ÊÓÈ°Ê $ISTANCES 9OUR HOUSE AND THE MALL ARE MILES APART ON THE SAME STRAIGHT ROAD Ê ££° ' AND ( | ]z / iÊi`«ÌÃÊvÊÌÜÊÃi}iÌÃÊ>ÀiÊ}Ûi°Ê`Êi>V ÊÃi}iÌÊi}Ì ° Ê/iÊÜ iÌ iÀÊÌ iÊÃi}iÌÃÊ>ÀiÊV}ÀÕḭ ] ] ] ] ] ] ] z q z #$zz z q z Óΰ ] ÊÓÓ°Ê !" Ê z ! " !"zz 23z 2 3 23zz z 45zz z CONGRUENT CONGRUENT ] ] #$z # $ 45z 4 5 ] ] Ó{° +,z + , Óx° /0z / 0 ] ] -.z- . 12z 1 2 ] ] ] ] ] M ÊÌ iÊ`>}À>]ÊÊÃÊÌ iÊ`«ÌÊvÊÌ iÊÃi}ḭÊ`ÊÌ iÊ `V>Ìi`Êi}Ì ° Ó£° YD &OR USE WITH PAGES n `ÊÌ iÊi}Ì ÊvÊÌ iÊÃi}ḭÊ/ iÊwÊ`ÊÌ iÊVÀ`>ÌiÃÊvÊÌ iÊ`«ÌÊ vÊÌ iÊÃi}ḭ CM ] Ê Î° 0OINT 4 BISECTS 56z &IND 56 IF 54 ]zYARDS Ê x°Ê &IND ,. *À>VÌViÊÊ CONTINUED ,%33/. &OR USE WITH PAGES n Ê BISECTS -.0 AND 1.3 ANGLE AND .2 >°Ê 7HICH ANGLES ARE ACUTE OBTUSE RIGHT L° )DENTIFY THE CONGRUENT ANGLES V° )F M1.2 lND M -.2 M 2.3 M1.3 AND M1.0 Óx°Ê>° !CUTE ANGLES -.1 1.2 2.3 AND 3.0 4HERE ARE NO OBTUSE ANGLES 2IGHT ANGLES -.2 AND 0.2 L° -.1 3.0 1.2 2.3 AND -.2 0.2 V° M -.2 zM 2.3 z M1.3 AND M1.0 'EOMETRY #HAPTER 2ESOURCE "OOK %
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