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

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