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