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PLANEANDSOLIDGEOMETRY
I. OverviewofCourse
ed
PlaneandSolidGeometryprovidesanindepthapproachtotheprinciplesofEuclideanGeometry.Thecourseemphasizesgeometricproofsrequiringthemasteryofdeductiveandinductivereasoningonthepartofthestudentsaswellasthedevelopmentoforganizedstudyskills.
II. SubjectAreasCoverA. BasicsofGeometry
1. PatternsandInductiveReasoning2. Points,Lines,andPlanes3.
SegmentsandTheirMeasures4. AnglesandTheirMeasures5.
SegmentandAngleBisectors6. AnglePairRelationships7.
IntroductiontoPerimeter,CircumferenceandArea
B. ReasoningandProof1. ConditionalStatements2.
DefinitionsandBiconditionalStatements3. DeductiveReasoning4.
ReasoningwithPropertiesofAlgebra5. ProvingStatementsaboutSegments6.
ProvingStatementsaboutAngles
C. PerpendicularandParallelLines1. LinesandAngles2.
ProofandPerpendicularLines3. ParallelLinesareParallel4.
ProvingLinesareParallel5. UsingPropertiesofParallelLines6.
ParallelLinesintheCoordinatePlane7.
PerpendicularLinesintheCoordinatePlane
D. CongruentTriangles1. TrianglesandAngles2.
CongruenceandTriangles3. ProvingTrianglesareCongruent4.
UsingCongruentTriangles5. Isosceles,Equilateral,andRightTriangles6.
TrianglesandCoordinateProof
E. PropertiesofTriangles1. PerpendicularBisectors2.
BisectorsofaTriangle3. MediansandAltitudesofaTriangle
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4. MidsegmentTheorem5. InequalitiesinOneTriangle6.
IndirectProofandInequalitiesinTwoTriangles
F. Quadrilaterals1. Polygons2. PropertiesofParallelograms3.
ProvingQuadrilateralsareParallelograms4.
Rhombuses,Rectangles,andSquares5. TrapezoidsandKites6.
SpecialQuadrilaterals7. AreasofTrianglesandQuadrilaterals
G. Transformations1. MotioninaPlane2. ReflectionsandRotations3.
TranslationsandVectors4. GlideReflectionsandCompositions
H. Similarity1. RatioandProportion2.
ProblemSolvinginGeometrywithProportions3.
SimilarPolygons/Triangles4. ProvingTrianglesareSimilar5.
ProportionsandSimilarTriangles6. Dilations
I. RightTrianglesandTrigonometry1. SimilarRightTriangles2.
ThePythagoreanTheorem3. SpecialRightTriangles4.
TrigonometricRatios5. SolvingRightTriangles6. Vectors
J. Circles1. TangentstoCircles2. ArcsandChords3.
InscribedAngles4. OtherAngleRelationshipsinCircles5.
EquationsofCircles6. Locus
K. AreaofPolygonsandCircles1. AngleMeasuresinPolygons2.
AreasofRegularPolygons3. PerimetersandAreasofSimilarFigures4.
CircumferenceandArcLength
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5. AreasofCirclesandSectors6. GeometricProbability
L. SurfaceAreaandVolume1. ExploringSolids2.
SurfaceAreaofPrismsandCylinders3. SurfaceAreaofPyramidsandCones4.
VolumeofPrismsandCylinders5. VolumeofPyramidsandCones6.
SurfaceAreaandVolumeofSpheres7. SimilarSolids
III. InstructionalObjectives
als
A.
TorecognizetheculturevalueandpleasureonecanderivefromGeometry.B.
Tobeusedasasteppingstoneformoreadvancedcourses.C.
Tomakethestudentsawareoftheimportanceofmathematicsintheireveryday
life.D.
TomakestudentsawareofthepossibleeverydayusageofGeometry.
IV. TextsandOtherCourseMateriA.
BasicTextbook:Geometry:Applying,ReasoningandMeasuring.2001McDougall
Littell.B. VisualAidsC.
Instruments(compass,protractor,straightedge)D. Calculator
