美国高中几何教材目录

　　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。

　　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。