Upload
others
View
12
Download
0
Embed Size (px)
Citation preview
Geometry and Measurement of Plane Figures
Activity Set 4
Trainer Guide
GEOMETRY AND MEASUREMENT OF PLANE FIGURES—AcTIvITY SET 4 Int_PGe_04_TGCopyright© by the McGraw-Hill Companies—McGraw-Hill Professional Development
GEOMETRY AND MEASUREMENT OF PLANE FIGURES—AcTIvITY SET 4 Int_PGe_04_TG
Copyright© by the McGraw-Hill Companies—McGraw-Hill Professional Development 1
GEOMETRY AND MEASUREMENT OF PLANE FIGURESACTIvITY SET #4
NGSSS 3.G.3.1 NGSSS 3.G.3.3 NGSSS 4.G.5.1 NGSSS 5.G.3.1
Amazing Angles
In this activity, participants explore angle concepts in polygon shapes.
Materials
• Transparency/Page:AngleTypes• Transparency/Page:MeasuringAngles• Transparency/Page:ACircleofMeasure• Transparency/Page:PolygonAnglesChart• Transparency/Page:PolygonAnglesChart
AnswerKey• plain 3 5 cards (4 per participant)• rulerforeachparticipant• protractorforeachparticipant• scissorsforeachparticipant• pens/pencils(multicolorpens)• blanktransparency
Vocabulary
• degree• angle• vertex• rightangle• straightangle
tiMe:30minutes
GEOMETRY AND MEASUREMENT OF PLANE FIGURES—AcTIvITY SET 4 Int_PGe_04_TG
Copyright© by the McGraw-Hill Companies—McGraw-Hill Professional Development 2
GEOMETRY AND MEASUREMENT OF PLANE FIGURESACTIvITY SET #4
INTRODUCE
•Remindparticipantsthatoneaspectofgeometryistheapplicationofanglestovariousshapesandfigures.
•DisplayTransparency:AngleTypes.
•Goovertheangledescriptionsandnames.
teaching tip: It may help to clarify the definitions if you explain the meaning of adjacent—having a common side or border and, in mathematics, a common endpoint.
•DisplayTransparency:MeasuringAngles and have participantstakeouttheirmatchingpages.
•Takeoutaprotractor.
•Demonstrateonangle1howtomeasureanangle.
◆ Alignthe0˚markandlinewiththeright-handsideoftheangle,makingsurethatthevertexoftheangleisalignedwiththecentermarkofthe0˚line.(Thereisusuallyasmallholeatthislocationtoenableyoutoplacethevertexappropriately.)
◆ Locatetheleft-handsideoftheangleandtracethelinetothedegreemarkontheprotractor.
•Haveparticipantsmeasuretheremaininganglesandwritethedegreesthattheyfindintheappropriateblanksontheirpages.
•Goovertheanswerswiththeparticipantsanddemonstratethemeasurementprocess,ifnecessary,toaddressanyquestions.
•Reviewthedefinitionsatthebottomofthepage.
interior angle an angle formed by two sidesof a polygon
adjacent angles angles that share a commonside and a common vertexbetween them, but that donot share any interior points
exterior angle an angle adjacent to, butoutside of, a polygon–formedby extending one side of thepolygon
angle types
McGraw-Hill Professional Development GEOMETRY AND MEASUREMENT OF PLANE FIGURES/31
A
B
C A
B
C
A
B
D
C
interior exterior adjacent
Transparency: Angle Types
acute angle—an angle less than 90º
obtuse angle—an angle more than 90º
right angle—an angle equal to 90º
straight angle—an angle of 180º
Measuring angles
McGraw-Hill Professional Development GEOMETRY AND MEASUREMENT OF PLANE FIGURES/33
1
45
23
angle 2 angle 3angle 1
angle 5angle 4
Transparency: Measuring Angles
GEOMETRY AND MEASUREMENT OF PLANE FIGURES—AcTIvITY SET 4 Int_PGe_04_TG
Copyright© by the McGraw-Hill Companies—McGraw-Hill Professional Development 3
GEOMETRY AND MEASUREMENT OF PLANE FIGURESACTIvITY SET #4
teaching tip: If time permits, have participant volunteers come to the front to measure the angles and record the results on the transparency.
teaching tip: If the group is advanced, have them also identify the angle type after they measure.
• 1—acuteangle• 2—acuteangleandadjacentangle(adjacentto
angle 3)• 3—obtuseangleandadjacentangle(adjacentto
angle2)• 4—straightangle(straightline)• 5—rightangle(formedbyperpendicularlines)
Ask why none of the angles are interior or exterior. (Theyarenotpartof,oradjacentto,polygons.)
•Askparticipantshowmanydegreesarearoundthecenterofacircle.
•DisplayTransparency:ACircleofMeasure.
•Pointouttoparticipantsthatthedistancearound thecenterofthecircle(360˚)isthebasisforallanglemeasure.
•Pointoutonthetransparencythatthediameterofthecircle(astraightline)dividestherevolutioninhalf,creatingastraightangle,or180˚.
•Explaintoparticipantsthattheywillusethisinformationtohelpthemfindthenumberofdegreesintheinterioranglesofatriangle.
It is a mathematics convention that the unit ofangle measure (degree) is 1
360 of a completerevolution around the center of a circle.
a circle of Measure
McGraw-Hill Professional Development GEOMETRY AND MEASUREMENT OF PLANE FIGURES/35
Transparency: A Circle of Measure
GEOMETRY AND MEASUREMENT OF PLANE FIGURES—AcTIvITY SET 4 Int_PGe_04_TG
Copyright© by the McGraw-Hill Companies—McGraw-Hill Professional Development 4
GEOMETRY AND MEASUREMENT OF PLANE FIGURESACTIvITY SET #4
DISCUSS AND DO
•Distributetoeachparticipantfour3 5 cards and a pairofscissors.
•Haveeachparticipantdrawononecardalarge triangle.
teaching tip: Have participants use a straightedge, ruler, or card side to draw all figures. Straightedges are required to achieve accuracy for the activity. Also, no shape that they create can have overlapping edges.
•Haveparticipantscutouttheirtriangles.
•Haveparticipantsuseapenorpenciltocolorintheanglesabout1
2outfromeachvertex.
•Havethemcutthetriangleinto3pieces,witheachpiececontaining1angle.
•Tellthemtolaythe3anglestogetherwiththeverticesjoiningandtheirsidestouching.
•Pointoutthattheynowhaveastraightlineorastraightangle,whichisdefinedas180˚.
•Pointoutthattheyallmadedifferentkindsoftriangles.
•Explainthattheanglesofalltrianglessumto180˚.
•Haveparticipantsusetheirrulerstodrawanothertriangleononeoftheir3 5 cards.
•Havethemmakethetrianglesaslargeaspossibleforeaseofmeasurement.
•Tellthemtomeasureeachangleintheirtriangles,usingtheirprotractors,andaddthethreeanglestogether.
GEOMETRY AND MEASUREMENT OF PLANE FIGURES—AcTIvITY SET 4 Int_PGe_04_TG
Copyright© by the McGraw-Hill Companies—McGraw-Hill Professional Development 5
GEOMETRY AND MEASUREMENT OF PLANE FIGURESACTIvITY SET #4
•Displayablanktransparency.
•Havevariousvolunteerparticipantssharetheanglemeasureswithintheirtriangles.
•Recordontheblanktransparencytheanglemeasuresas they are shared.
•Pointoutthattheanglesdifferedindividually, butthatthesumoftheanglesforanytriangle wasalways180˚.
•Haveparticipantstakeouttheirthirdcards.
•Pointoutthatthecardisarectangle.
•Askthemtocolorthe4cornersandcutthecardinto4pieces(1cornertoeachpiece).
•Askthemtoarrangethecornerstogetherandtell youhowmanydegreesthereareintheanglesof arectangle.(360˚)
•Explainthatanyquadrilateralhasanglesthatsum to360˚.
•Drawarectangleonablanktransparency.
•Drawadiagonalfromonecorneroftherectangletothe corner opposite.
•Pointoutthattheanglesofthe2trianglesthusformedalsosumto360˚.
•Haveparticipantsdrawa5-sidedfigureontheir last cards.
•Havethemcolorthecornerangles,cutouttheshape,andthencutitinto5pieces—1angleperpiece.
•Askparticipantstolaytheanglestogetherinsuchawaythattheycantellyouthetotalnumberofdegrees.
•Suggestthat,whenparticipantscomplainthattheycannotmatchalltheangles,theycreatemorethanonefigure.
GEOMETRY AND MEASUREMENT OF PLANE FIGURES—AcTIvITY SET 4 Int_PGe_04_TG
Copyright© by the McGraw-Hill Companies—McGraw-Hill Professional Development 6
GEOMETRY AND MEASUREMENT OF PLANE FIGURESACTIvITY SET #4
•Askparticipantshowmanydegreesthereareintheanglesofapentagon.(540˚)
•Haveoneparticipantcomeupwithhisorhershapesandillustrateontheoverheadprojectorhisorhersolution.
•Drawa5-sidedpolygononablanktransparency.
•Draw,from1vertex,linestoallopposingverticesforwhichyoucanmaketriangles.
•Pointoutthattheanglesofthe3trianglesthusformedalsosumto540˚.
CONCLUDE
•DisplayTransparency:PolygonAnglesChartand have participantstakeouttheirmatchingpages.
•Fillin,alongwiththeparticipants,thefirstthreerowsofthePolygonAnglesChartusinginformationthattheyhavecollectedduringthisactivity.
•Encourageparticipantstocreatetrianglesofeachshapetohelpthem.
•Askparticipantsthenumberofdegreesthattheythinktheanglesofahexagonwouldtotal.(720˚)
•Completethehexagonrowonthechart.
•Askparticipantsiftheyrecognizeapattern. (Theruleis(n–2)•180˚.)
•Askparticipantshowthisruleisderived. (n,thenumberofsides,less2isthenumber ofnon-overlappingtrianglesineachshape.)
GEOMETRY AND MEASUREMENT OF PLANE FIGURES—AcTIvITY SET 4 TRANS_K6_PG_04Copyright© 2002 by the McGraw-Hill Companies—McGraw-Hill Professional Development
triangle
quadrilateral
pentagon
hexagon
heptagon
octagon
nonagon
decagon
Polygon Number of Number of Sides Number of Degrees: Name Sides Minus 2
polygon angles chart
Transparency: Polygon Angles Chart
GEOMETRY AND MEASUREMENT OF PLANE FIGURES—AcTIvITY SET 4 Int_PGe_04_TG
Copyright© by the McGraw-Hill Companies—McGraw-Hill Professional Development 7
GEOMETRY AND MEASUREMENT OF PLANE FIGURESACTIvITY SET #4
•Writetheruleonthetransparencyinthefourthcolumnheading.
•Godowntothelastfiguresonthechart.
•Askparticipantsforthenumberofdegreesat eachrow.
•Fillinthetransparencyateachstep.
•RefertoTransparency:PolygonAnglesChartAnswerKey, as necessary.
End of Amazing AnglesGEOMETRY AND MEASUREMENT OF PLANE FIGURES—AcTIvITY SET 4 TRANS_K6_PG_04Copyright© 2002 by the McGraw-Hill Companies—McGraw-Hill Professional Development
n n – 2 (n – 2) • 180°
3
4
5
6
7
8
9
10
1 180°
2 360°
3 540°
4 720°
5 900°
6 1,080°
7 1,260°
8 1,440°
triangle
quadrilateral
pentagon
hexagon
heptagon
octagon
nonagon
decagon
Polygon Number of Number of Sides Number of Degrees: Name Sides Minus 2
polygon angles chart Answer Key
Transparency: Polygon Angles Chart Answer Key
GEOMETRY AND MEASUREMENT OF PLANE FIGURES—AcTIvITY SET 4 Int_PGe_04_TG
Copyright© by the McGraw-Hill Companies—McGraw-Hill Professional Development 8
GEOMETRY AND MEASUREMENT OF PLANE FIGURESACTIvITY SET #4
Race to Place
Inthisactivity,participantsusegeometricknowledgethattheyremembertomatchpicturesofanglesandshapeswiththeirdefinitions.
Materials
• Transparency/Page:RacetoPlaceDirections• Transparency/Page:TriangleFactsAnswerKey• Transparency/Page:AngleFactsAnswerKey• Transparency/Page:AnglesinShapesAnswerKey• Transparency/Page:LineFactsAnswerKey• Transparency/Page:CircleFactsAnswerKey• RacetoPlaceCards• 5pocketcharts• bell
tiMe:15minutes
teaching tip: Post the pocket charts with their definitions before the beginning of the activity. Use the Facts transparencies as a guide for the definitions that go with each title. Space the charts around the room with a lot of room between them.
GEOMETRY AND MEASUREMENT OF PLANE FIGURES—AcTIvITY SET 4 Int_PGe_04_TG
Copyright© by the McGraw-Hill Companies—McGraw-Hill Professional Development 9
GEOMETRY AND MEASUREMENT OF PLANE FIGURESACTIvITY SET #4
INTRODUCE
•Suggesttoparticipantsthatovertimetheyhaveaccumulatedalotofknowledgeaboutthewaylines,shapes,andangleswork.
•Pointoutthefivechartsandtheirdefinitions.
•Explaintotheparticipantsthattheywillcompeteasteamstomatchgeometricdefinitionswithpicturesthatillustratetheconceptsdefined.
teaching tip: If you have a large group, assign pairs instead of single people to each card.
DISCUSS AND DO
•DisplayTransparency:RacetoPlaceDirections.
•Gooverthestepsofthegame.
•Haveparticipantsmoveinto4or5equal-sizedgroups.
•Distributetheshapecards—allofonecoloredshape toeachgroup,onecardperperson.
•Call,“Go.”
•Havethefirstgrouptofinishsendonemembertothefrontoftheroomtoringthebell.
teaching tip: If a team member cannot place his or her shape card, he or she should go to the end of the line and wait to place the card after other team members have placed their cards.
teaching tip: If the group is inexperienced, permit them a few moments to look at the definition sheets(AnswerKeys)beforethegame.
GEOMETRY AND MEASUREMENT OF PLANE FIGURES—AcTIvITY SET 4 TRANS_K6_PG_04Copyright© 2002 by the McGraw-Hill Companies—McGraw-Hill Professional Development
Directions• Distribute your team cards evenly among the members
of your team.
• Have team members play their cards in relay fashion.
• Have a player:
• race to the chart that holds the definition of the picture on his or her card
• place the card next to the definition
• race back to the team and sit down
• Have the next person race to the chart and place his orher card.
• Have one team member race to the front and ring thebell when all the team’s cards are correctly placed.
race to place
Transparency: Race to Place Directions
GEOMETRY AND MEASUREMENT OF PLANE FIGURES—AcTIvITY SET 4 Int_PGe_04_TG
Copyright© by the McGraw-Hill Companies—McGraw-Hill Professional Development 10
GEOMETRY AND MEASUREMENT OF PLANE FIGURESACTIvITY SET #4
CONCLUDE
•Congratulatetheparticipantsforbeingabletoremembersomanygeometryconceptsanddefinitions.
•DisplaytheAnswerKeytransparenciesinturn,quicklyreviewingthedefinitions.
•Emphasizethefollowingdefinitionsforeachkey:
◆ Transparency:TriangleFactsAnswerKey –equilateraltriangle –righttriangle(especiallyhypotenuse)
◆ Transparency:AngleFactsAnswerKey –straight angle –vertical angles
◆ Transparency:AnglesinShapesAnswerKey –triangle –equilateraltriangle
◆ Transparency:LineFactsAnswerKey –alternate interior angles
◆ Transparency:CircleFactsAnswerKey –circumference
End of Race to Place
McGraw-Hill Professional Development GEOMETRY AND MEASUREMENT OF PLANE FIGURES/73
• A scalene triangle has no congruent sides and no congruent angles.
• An isosceles triangle has 2 congruent sides and 2 congruent angles.
• An equilateral triangle has 3 congruent sides and 3 congruent angles.
• The angles of an acute triangle areall less than 90˚.
• One angle in an obtuse triangle is greater than 90˚.
• A right triangle has one angle equal to 90˚. The side opposite the 90˚ angle is called the hypotenuse.
triangle Facts Answer Key
Transparencies: Triangle Facts Answer Key, Angle Facts Answer Key, Angles in Shapes Answer Key, Line Facts Answer Key, Circle Facts Answer Key
GEOMETRY AND MEASUREMENT OF PLANE FIGURES—AcTIvITY SET 4 Int_PGe_04_PMCopyright© by the McGraw-Hill Companies—McGraw-Hill Professional Development
interior angle an angle formed by two sides of a polygon
adjacent angles angles that share a common side and a common vertex between them, but that do not share any interior points
exterior angle an angle adjacent to, but outside of, a polygon—formed by extending one side of the polygon
Angle Types
A
B
C A
B
C
A
B
D
C
interior exterior adjacent
GEOMETRY AND MEASUREMENT OF PLANE FIGURES—AcTIvITY SET 4 Int_PGe_04_PMCopyright© by the McGraw-Hill Companies—McGraw-Hill Professional Development
acute angle—an angle less than 90º
obtuse angle—an angle more than 90º
right angle—an angle equal to 90º
straight angle—an angle of 180º
Measuring Angles
1
45
23
angle 2 angle 3angle 1
angle 5angle 4
GEOMETRY AND MEASUREMENT OF PLANE FIGURES—AcTIvITY SET 4 Int_PGe_04_PMCopyright© by the McGraw-Hill Companies—McGraw-Hill Professional Development
It is a mathematics convention that the unit of angle measure (degree) is 1
360 of a complete revolution around the center of a circle.
A Circle of Measure
GEOMETRY AND MEASUREMENT OF PLANE FIGURES—AcTIvITY SET 4 Int_PGe_04_PMCopyright© by the McGraw-Hill Companies—McGraw-Hill Professional Development
triangle
quadrilateral
pentagon
hexagon
heptagon
octagon
nonagon
decagon
Polygon Number of Number of Sides Number of Degrees: Name Sides Minus 2
Polygon Angles Chart
GEOMETRY AND MEASUREMENT OF PLANE FIGURES—AcTIvITY SET 4 Int_PGe_04_PMCopyright© by the McGraw-Hill Companies—McGraw-Hill Professional Development
n n – 2 (n – 2) • 180°
3
4
5
6
7
8
9
10
1 180°
2 360°
3 540°
4 720°
5 900°
6 1,080°
7 1,260°
8 1,440°
triangle
quadrilateral
pentagon
hexagon
heptagon
octagon
nonagon
decagon
Polygon Number of Number of Sides Number of Degrees: Name Sides Minus 2
Polygon Angles Chart Answer Key
GEOMETRY AND MEASUREMENT OF PLANE FIGURES—AcTIvITY SET 4 Int_PGe_04_PMCopyright© by the McGraw-Hill Companies—McGraw-Hill Professional Development
Directions •Distributeyourteamcardsevenlyamongthemembersofyourteam.
•Haveteammembersplaytheircardsinrelayfashion.
•Haveaplayer:
• racetothechartthatholdsthedefinitionofthe pictureonhisorhercard
• placethecardnexttothedefinition
• racebacktotheteamandsitdown
•Havethenextpersonracetothechartandplacehisorhercard.
•Haveoneteammemberracetothefrontandringthebellwhenalltheteam’scardsarecorrectlyplaced.
Race to Place
GEOMETRY AND MEASUREMENT OF PLANE FIGURES—AcTIvITY SET 4 Int_PGe_04_PMCopyright© by the McGraw-Hill Companies—McGraw-Hill Professional Development
• Ascalenetrianglehasnocongruentsidesandnocongruentangles.
• Anisoscelestrianglehas2congruentsidesand2congruentangles.
• Anequilateral trianglehas3congruentsidesand3congruentangles.
• Theanglesofanacute trianglearealllessthan90˚.
• Oneangleinanobtuse triangleisgreaterthan90˚.
• Aright trianglehasoneangleequalto90˚.Thesideoppositethe90˚angleiscalledthehypotenuse.
Triangle Facts Answer Key
GEOMETRY AND MEASUREMENT OF PLANE FIGURES—AcTIvITY SET 4 Int_PGe_04_PMCopyright© by the McGraw-Hill Companies—McGraw-Hill Professional Development
• Anacute angleislessthan90˚.
• Anobtuse angleisgreaterthan90˚andlessthan180˚.
• Astraight angleisequalto180˚.
• Aright angleisequalto90˚.
• Anglesthatshareacommonsidebetweenthemareadjacent.
• Twoanglesthatsumto180˚arecalledsupplementary.
• Nonadjacentanglesformedbytwointersectinglinesarecalledvertical angles.Theyhavethesamemeasure.
Angle FactsAnswer Key
GEOMETRY AND MEASUREMENT OF PLANE FIGURES—AcTIvITY SET 4 Int_PGe_04_PMCopyright© by the McGraw-Hill Companies—McGraw-Hill Professional Development
• Atrianglehasanglesthatsumto180˚.
• Arectanglehasanglesthatsumto360˚.
• Anglesinsideashapeareinterior angles.
• Anglesoutsideashapeareexterior angles.
• Thebaseanglesandoppositesidesofanisoscelestrianglearecongruent.
• Thesidesandanglesofanequilateraltrianglearecongruent.
Angles in Shapes Answer Key
GEOMETRY AND MEASUREMENT OF PLANE FIGURES—AcTIvITY SET 4 Int_PGe_04_PMCopyright© by the McGraw-Hill Companies—McGraw-Hill Professional Development
• Asetofpoints,astraightpath,thatextendsindefinitelyin2oppositedirectionsisaline.
• Aline segmentis2endpointsandthestraightpathbetweenthem.
• Perpendicularlinesformrightangles.
• Ifalineintersectstwoparallellines,thealternate interior anglesareequal.
• Parallellinesareequidistantfromeachother.
Line FactsAnswer Key
6 cm6 cm
GEOMETRY AND MEASUREMENT OF PLANE FIGURES—AcTIvITY SET 4 Int_PGe_04_PMCopyright© by the McGraw-Hill Companies—McGraw-Hill Professional Development
• Acompleterevolutionaroundthecenterofacirclehas360º.
• Achordisalinesegmentthatconnectstwopointsonthecircumferenceofacircle.
• Thelinesegmentjoiningthecenterofthecircleandapointonitscircumferenceiscalledaradius.
• Adiameter isachordthatpassesthroughthecenterofacircle.Itslengthistwicethatoftheradiusofthecircle.
• Acircleisthesetofallpointsinaplanethatareequidistantfromaspecifiedpoint.
• Thedistancearoundacircleiscalleditscircumference.
Circle Facts Answer Key
GEOMETRY AND MEASUREMENT OF PLANE FIGURES—AcTIvITY SET 4 Int_PGe_04_PMCopyright© by the McGraw-Hill Companies—McGraw-Hill Professional Development
GlossaryGeometry and Measurement of Plane Figures
angle Geometricfiguremadeof2raysor2linesegmentsthatsharethesameendpoint,calledavertex.
area Thenumberofsquareunitsinaregion.
congruent Havingthesameshape,size,and/ormeasure.
degree Aunitformeasuringangles.
irregular polygon Apolygoninwhichnotallthesidesarecongruentand/ornotalltheangleshavethesamemeasure.
line Asetofpointsformingastraightpathin2directionsthatareoppositeeachother.
perimeter Thedistancearoundtheoutsideofashapeorfigure.
plane Aflatsurfacethatextendsforeverinalldirections.
point Alocationinspace.
polygon Aclosedshapemadeupofaminimumof3linesegments.
quadrilateral Apolygonwith4sides.
rectangle Aquadrilateralwith4rightangles.
GEOMETRY AND MEASUREMENT OF PLANE FIGURES—AcTIvITY SET 4 Int_PGe_04_PMCopyright© by the McGraw-Hill Companies—McGraw-Hill Professional Development
regular polygon Apolygoninwhichallthesidesarecongruentandalltheangleshavethesamemeasure.
triangle Apolygonwith3sides.
Glossary (continued)
GEOMETRY AND MEASUREMENT OF PLANE FIGURES—AcTIvITY SET 4 Int_PGe_04_PMCopyright© by the McGraw-Hill Companies—McGraw-Hill Professional Development
Rac
e to
Pla
ce C
ard
s (1
of
20
)
GEOMETRY AND MEASUREMENT OF PLANE FIGURES—AcTIvITY SET 4 Int_PGe_04_PMCopyright© by the McGraw-Hill Companies—McGraw-Hill Professional Development
Rac
e to
Pla
ce C
ard
s (2
of
20
)
6 cm6 cm
GEOMETRY AND MEASUREMENT OF PLANE FIGURES—AcTIvITY SET 4 Int_PGe_04_PMCopyright© by the McGraw-Hill Companies—McGraw-Hill Professional Development
Rac
e to
Pla
ce C
ard
s (3
of
20
)
GEOMETRY AND MEASUREMENT OF PLANE FIGURES—AcTIvITY SET 4 Int_PGe_04_PMCopyright© by the McGraw-Hill Companies—McGraw-Hill Professional Development
Rac
e to
Pla
ce C
ard
s (4
of
20
)
GEOMETRY AND MEASUREMENT OF PLANE FIGURES—AcTIvITY SET 4 Int_PGe_04_PMCopyright© by the McGraw-Hill Companies—McGraw-Hill Professional Development
Rac
e to
Pla
ce C
ard
s (5
of
20
)
GEOMETRY AND MEASUREMENT OF PLANE FIGURES—AcTIvITY SET 4 Int_PGe_04_PMCopyright© by the McGraw-Hill Companies—McGraw-Hill Professional Development
Rac
e to
Pla
ce C
ard
s (6
of
20
)
GEOMETRY AND MEASUREMENT OF PLANE FIGURES—AcTIvITY SET 4 Int_PGe_04_PMCopyright© by the McGraw-Hill Companies—McGraw-Hill Professional Development
Rac
e to
Pla
ce C
ard
s (7
of
20
)
GEOMETRY AND MEASUREMENT OF PLANE FIGURES—AcTIvITY SET 4 Int_PGe_04_PMCopyright© by the McGraw-Hill Companies—McGraw-Hill Professional Development
Rac
e to
Pla
ce C
ard
s (8
of
20
)
GEOMETRY AND MEASUREMENT OF PLANE FIGURES—AcTIvITY SET 4 Int_PGe_04_PMCopyright© by the McGraw-Hill Companies—McGraw-Hill Professional Development
Rac
e to
Pla
ce C
ard
s (9
of
20
)
GEOMETRY AND MEASUREMENT OF PLANE FIGURES—AcTIvITY SET 4 Int_PGe_04_PMCopyright© by the McGraw-Hill Companies—McGraw-Hill Professional Development
Rac
e to
Pla
ce C
ard
s (1
0 o
f 2
0)
A complete revolution around the center of a
circle has 360º.
A chord is a line segment that connects two points
on the circumference of a circle.
The line segment joining the center of the circle and
a point on its circumference is called a radius.
GEOMETRY AND MEASUREMENT OF PLANE FIGURES—AcTIvITY SET 4 Int_PGe_04_PMCopyright© by the McGraw-Hill Companies—McGraw-Hill Professional Development
Rac
e to
Pla
ce C
ard
s (1
1 o
f 2
0)
Ifalineintersectstwoparallellines,the
alternate interior angles areequal.
Parallel linesareequidistantfromeachother.
Aright angle isequalto90°.
GEOMETRY AND MEASUREMENT OF PLANE FIGURES—AcTIvITY SET 4 Int_PGe_04_PMCopyright© by the McGraw-Hill Companies—McGraw-Hill Professional Development
Rac
e to
Pla
ce C
ard
s (1
2 o
f 2
0)
Asetofpointsthatextendindefinitelyin2oppositedirectionsisaline.
Aline segment hastwoendpoints.
Perpendicular linesformrightangles.
GEOMETRY AND MEASUREMENT OF PLANE FIGURES—AcTIvITY SET 4 Int_PGe_04_PMCopyright© by the McGraw-Hill Companies—McGraw-Hill Professional Development
Rac
e to
Pla
ce C
ard
s (1
3 o
f 2
0)
Anglesoutsideashapeareexterior angles.
Thebaseanglesandoppositesidesofan
isosceles trianglearecongruent.
Thesidesandanglesofanequilateral triangle
arecongruent.
GEOMETRY AND MEASUREMENT OF PLANE FIGURES—AcTIvITY SET 4 Int_PGe_04_PMCopyright© by the McGraw-Hill Companies—McGraw-Hill Professional Development
Rac
e to
Pla
ce C
ard
s (1
4 o
f 2
0)
Atriangle hasanglesthatsumto180˚.
Arectangle hasanglesthatsumto360˚.
Anglesinsideashapeareinterior angles.
GEOMETRY AND MEASUREMENT OF PLANE FIGURES—AcTIvITY SET 4 Int_PGe_04_PMCopyright© by the McGraw-Hill Companies—McGraw-Hill Professional Development
Rac
e to
Pla
ce C
ard
s (1
5 o
f 2
0)
Non adjacent angles formed by two intersecting
lines are called vertical angles. They have the
same measure.
Angles that share a common side between
them are adjacent.
Two angles that sum to 180˚ are called
supplementary.
GEOMETRY AND MEASUREMENT OF PLANE FIGURES—AcTIvITY SET 4 Int_PGe_04_PMCopyright© by the McGraw-Hill Companies—McGraw-Hill Professional Development
Rac
e to
Pla
ce C
ard
s (1
6 o
f 2
0)
Anacute angle islessthan90˚.
Anobtuse angle isgreaterthan90˚andlessthan180˚.
Astraight angle isequalto180˚.
GEOMETRY AND MEASUREMENT OF PLANE FIGURES—AcTIvITY SET 4 Int_PGe_04_PMCopyright© by the McGraw-Hill Companies—McGraw-Hill Professional Development
Rac
e to
Pla
ce C
ard
s (1
7 o
f 2
0)
Theanglesofanacute triangle areall
lessthan90˚.
Oneangleinanobtuse triangle isgreaterthan90˚.
Aright triangle hasoneangleequalto90˚.
GEOMETRY AND MEASUREMENT OF PLANE FIGURES—AcTIvITY SET 4 Int_PGe_04_PMCopyright© by the McGraw-Hill Companies—McGraw-Hill Professional Development
Rac
e to
Pla
ce C
ard
s (1
8 o
f 2
0)
Thediameterisachordthatpassesthroughthecenterofacircle.
Acircle isthesetofallpointsinaplanethatareequidistantfromaspecifiedpoint.
Thedistancearoundacircleiscalleditscircumference.
GEOMETRY AND MEASUREMENT OF PLANE FIGURES—AcTIvITY SET 4 Int_PGe_04_PMCopyright© by the McGraw-Hill Companies—McGraw-Hill Professional Development
Rac
e to
Pla
ce C
ard
s (1
9 o
f 2
0)
Ascalene triangle hasnocongruentsidesandnocongruentangles.
Anisosceles triangle has2congruentsidesand2congruentangles.
Anequilateral triangle has3congruentsidesand3congruentangles.
GEOMETRY AND MEASUREMENT OF PLANE FIGURES—AcTIvITY SET 4 Int_PGe_04_PMCopyright© by the McGraw-Hill Companies—McGraw-Hill Professional Development
Rac
e to
Pla
ce C
ard
s (2
0 o
f 2
0)