美国中学数学教材(美国高中几何词汇汇总)

  美国高中几何课程主要学习几何定义、定理和特征。该课程通过考虑图形在坐标平面上的变换,发展了三角形同余和相似的概念。课程包括变换、同余、证明、构造、相似、直角三角形、三角学、面积、体积、几何建模、坐标几何、圆和抛物线等主题。

美国高中几何教材目录

  Ch.1 – Transformations, Congruence, Proof, and Constructions

  The Language of Geometry

  Transformations in the Coordinate Plane

  Symmetry

  Properties of Transformations

  Composition of Transformations

  Congruent Figures Defined in Terms of Rigid Motions

  Congruent Parts of Congruent Triangles

  Triangle Congruence Criteria

  Constructions 1.1

  Special Pairs of Angles

  Angles Formed by Parallel Lines Cut by Transversal

  Angles in a Triangle

  Isosceles Triangles

  The Triangle Inequality Theorem

  Angle Side Relationships in Triangles

  Properties of Parallelograms

  Special Quadrilaterals

  Making Conclusions and Developing Proofs

  Proofs Based on Congruent Triangles

  Constructions 1.2

  Line Segments in Triangles

  Constructions 1.3

  Unit Assessment: Transformations, Congruence, Proof, and Constructions

  Ch.2 – Similarity, Right Triangles and Trigonometry

  Properties of Dilations

  Similarity Transformations and Triangles

  Constructions 2.1

  AA Similarity in Triangles

  SSS~ and SAS~ Similarity

  The Splitter Theorems

  Similar Right Triangles

  Triangles: Congruence and Similarity

  The Special (Reference) Triangles

  Constructions 2.2

  Define Trigonometric Ratios in Right Triangles

  Relating Sine and Cosine

  Applications of Trigonometric Ratios and the Pythagorean Theorem

  Unit Assessment: Similarity, Proof, and Trigonometry

  Ch.3 – Geometric Measurement and Dimension

  Apply Geometric Principles to Solve for Perimeter and Area

  Apply Geometric Principles to the Area and Circumference of Circles

  Areas of Regular Polygons

  Identifying the Parts of Solid Figures

  Cross Sections of Solids

  Volume of Prisms & Cylinders

  Volume of Pyramids, Cones, and Spheres

  Cavalieri’s Principle

  Surface Area of Solids

  Rotational Volume

  Describe Objects Geometrically and Apply Concepts of Density

  Solving Design Problems with Geometry

  Unit Assessment: Geometric Measurement and Dimension

  Ch.4 – Expressing Geometric Properties with Equations (Analytic Geometry)

  Connecting Algebra and Geometry Through Coordinates

  Proving the Slope Criteria of Parallel and Perpendicular Lines

  Perpendicular Bisectors

  Proving Triangles in the Coordinate Plane

  Constructions 4.1

  Proving Quadrilaterals in the Coordinate Plane

  Constructions 4.2

  Partitioning Line Segments into a Given Ratio

  Area and Perimeter of Figures in the Coordinate Plane

  Focus-Directrix Definition of a Parabola

  Unit Assessment: Expressing Geometric Properties with Equations (Analytic Geometry)

  Ch.5 – Circles

  The Equation of a Circle in the Coordinate Plane

  Completing the Square to Determine the Center and Radius of a Circle

  Proving Points Lie on a Circle in the Coordinate Plane

  Intersecting Chords, Secants, and Tangents

  Chords in Circles

  Line Segments in a Circle

  Constructions 5.1

  Characteristics of Angles in Inscribed Polygons

  Tangent Lines in Circles

  Constructions 5.2

  Circles are Similar

  Constructions 5.3

  Arc Length and Area of Sectors (in Radians)

  Unit Project: Construct a 9-Point Circle

  Unit Assessment: Circles

 以上就是有关美国高中几何教材目录,希望对大家有帮助。英国得高中生,十一年级开始学习几何学,很多中国学生认为美国高中数学太简单,其实这是一种误区,在美国高中对数学感兴趣的数学基础好的学生,他们都在上AP课程,里面包含得微积分课,是国内的高中生却远远没有涉及到。

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