**Perimeter, Area, and Volume** (Focus on Transformation Methods)

- Area and Perimeter of Squares and Rectangles ()
- Area of Parallelogram
- Area of Triangle
- Area of Trapezoid
- Circumference of Circles
- Length of Arcs
- Area of Circles
- Area of Sectors
- Circle and Other Shapes
- Solid Figures and Their Nets
- Exploring the Nets of Rectangular Prisms and Cuboids
- Surface Area of Solid Figures
- Volume of Solid Figures
- Volume of Composite Solid Figures

**Rectangular Prism: Exploring Point, Line, and Plane**

- Elements of a Rectangular Prism: Face, Edge, and Vertex
- Draw Rectangular Prism
- The Positional Relationship Between Edges and Edges in a Cuboid
- The Positional Relationship Between Edges and Faces in a Cuboid
- The Positional Relationship Between Faces and Faces in a Cuboid

**Transformation**

- Translation
- Rotation
- Rotational Symmetry and Central Symmetry Figures
- Two Figures Form Central Symmetry
- Reflection and Reflectional Symmetry Figures
- Two Figures Form Reflectional Symmetry
- What Shapes and Combination of Shapes Can Form Tessellation
- Design Tessellation (with Art teacher)
- Figure Out the Geometry of Chinese Paper Cutting Art (with Art teacher)

**Geometric Proof – Parallel Lines**

- Recognize the Angles Formed by Two Lines and A Transversal
- Identify Parallel Lines
- Properties of Parallel Lines

**Geometric Proof – Congruent Triangles**

- The Sum of Interior Angles of Triangle
- Define Congruency and Congruent Trianles
- Exploring through Construction the Elements Necessary for Identifying Congruent Triangles (i.e., why AAA fails?)
- Identify Congruent Triangles by SAS
- Identify Congruent Triangles by AAS
- Identify Congruent Triangles by SSS
- Properties of Isosceles Triangles
- Identify Isosceles Triangles
- Equilateral Triangles and Related Proof

**Geometric Proof – Bisectors and Distance**

- Perpendicular Bisector
- Angle Bisector
- Trajectory and Construction
- Identify Congruent Right Triangles by HL
- Properties of Right Triangles and Related Proof
- Pythagorean Theorem (with 100 methods)
- Distance between Two Points

**Geometric Proof – Quadrilaterals**

- The Sum of Interior Angles and Exterior Angles of Polygons
- Properties of Parallelograms
- Identify Parallelograms using Three Methods
- Properties of Rectangles
- Identify Rectangles
- Folding Rectangles and Related Proof
- Properties of Rhombus
- Identify Rhombus
- Identify Squares
- Trapezoid ands Its Properties
- Isosceles Trapezoid and Related Proof
- Mid-segments of Triangles
- Mid-segments of Trapezoids

**Geometric Proof – Similar Triangles**

- Dilation and similar shapes
- Proportional segments
- Line parallel to a side of a triangle
- Identify similar triangles
- Properties of similar triangles
- Multiplication of vector by real numbers
- Linear transformation of plane vectors
- Meaning of trigonometric ratio
- Find trigonometric ratio in right triangles 25.3 Solve right triangles
- Application of Right triangles

**Geometric Proof – Circles**

- Confirm a Circle
- Relationship between Central Angle, Arch, Chord, and the Distance between Chord and the Center
- Chord of Circle Theorem
- Positional Relationship between A Line and A Circle
- Positional Relationship between Circles
- Regular Polygons and Circles

**Challenging Comprehensive Geometric Problems**

- 2018 Zhongkao Mathematics Question 25
- 2018 Zhongkao Mathematics Question 25
- 2019 Zhongkao Mathematics Question 25
- 2022 Zhongkao Mathematics Question 25
- 2023 Zhongkao Mathematics Question 25