Unit 0: Geometry Prerequisites
Summer Packet
Unit 1: Basic Geometry & Constructions
Video 1: Topic 1.1 Points, Lines, and Planes | The Foundation of Geometry
Video 2: Topic 1.2 Measuring Segments in Geometry | Segment Addition Postulate & Finding Missing Lengths
Video 3: Topic 1.3 How to Measure Angles in Geometry | Finding Missing Angle Measures
Video 4: Topic 1.4 Complementary, Supplementary, Vertical, Adjacent, Corresponding, Alternate Interior & Exterior Angles, Same Side Interior & Exterior Angles
Video 5: Topic 1.5 9 Geometric Constructions You Must Know
Unit 2: Reasoning & Proofs
Video 6: Topic 2.1 Patterns and Conjectures in Geometry | Inductive Reasoning & Real-Life Examples
Video 7: Topic 2.2 Conditional Statements & Truth Tables | Master Logic in Geometry
Video 8: Topic 2.3 Biconditionals & Definitions | Classify Undefined Terms, Conjectures, Postulates & Theorems
Video 9: Topic 2.4 Deductive Reasoning: Law of Detachment & Law of Syllogism Explained
Video 10: Topic 2.5 Reasoning in Algebra and Geometry | How to Write a Two-Column Proof
Video 11: Topic 2.6 Proving Angles Congruent Using 2-Column Proof & Paragraph Proof
Unit 3: Parallel, Perpendicular, Skew Lines & Planes
Video 12: Topic 3.1 Lines and Angles in Geometry | Parallel Lines, Skew Lines, Parallel Planes & More
Video 13: Topic 3.2 Properties of Parallel Lines | Corresponding, Alternate Interior & Same-Side Interior Angles
Video 14: Topic 3.3 Proving Lines Parallel Using Paragraph Proofs & Flowchart Proofs
Video 15: Topic 3.4 Parallel and Perpendicular Lines | Three Parallel Lines Theorem & Perpendicular Line Theorems
Video 16: Topic 3.5 Parallel Lines and Triangles | Triangle Angle Sum, Exterior Angle Theorems & Parallel Postulate
Video 17: Topic 3.6: Determine the Slopes/Rate of Change of Linear Functions.
Video 18: Topic 3.7: Write the Equations of Parallel & Perpendicular Lines.
Unit 4: Congruent Triangles
Video 19: Topic 4.1 Congruent Figures | Overlapping Angles, Overlapping Segments & Third Angles Theorem
Video 20: Topic 4.2 Triangle Congruence by SSS-SAS Theorems
Video 21: Topic 4.3 Triangle Congruence by ASA-AAS Theorems
Video 22: Topic 4.4 Triangle Congruence by HL Theorems & CPCTC
Video 23: Topic 4.5 Isosceles & Equilateral Triangles | Theorems, Proofs, and Geometry Problems
Video 24: Topic 4.6 Constructing Right Triangles, Isosceles Triangles, Isosceles Right Triangles, and Equilateral Triangles
Video 25: Topic 4.7 Congruence in Overlapping Triangles
Unit 5: Relationships within Triangles
Video 25: Topic 5.1 Midpoint - Distance - Partition of the Line Segment
Video 26: Topic 5.2 Midsegments of Triangles | Triangle Midsegment Theorem
Video 27: Topic 5.3 Perpendicular & Angle Bisectors in Triangles | Proofs, Theorems & Examples
Video 28: Topic 5.4 Circumcenter & Incenter Theorems | Concurrency of Perpendicular Bisectors and Angle Bisectors in Triangles
Video 29: Topic 5.5A Centroid & Orthocenter Theorems | Concurrency of Medians & Altitudes in Triangles
Video 30: Topic 5.5B Trick to Memorize the Circumcenter, Incenter, Centroid & Orthocenter
Video 31: Topic 5.6 Constructing the Circumcenter, Incenter, Centroid & Orthocenter | Geometry Constructions
Video 32: Topic 5.7 Indirect Proof (Proof by Contradiction)
Video 33: Topic 5.8 Inequalities in One Triangle | Side-Angle Relationships & Triangle Inequality Theorem
Video 34: Topic 5.9 Inequalities in Two Triangles | Hinge Theorem & Converse Explained
Unit 6: Polygons & Quadrilaterals
Video 33: Topic 6.1 Polygon Angle-Sum Theorems & Exterior Angle-Sum Theorem
Video 34: Topic 6.2 Properties of Parallelograms | Theorems, Proofs & Geometry Examples
Video 35: Topic 6.3 Conditions for Parallelograms | Proving a Quadrilateral is a Parallelogram
Video 36: Topic 6.4 Properties of Rhombuses, Rectangles & Squares | Geometry Theorems, Proofs & Examples
Video 37: Topic 6.5 Conditions for Rhombuses, Rectangles & Squares | Proving Special Quadrilaterals
Video 38: Topic 6.6 Trapeziums & Kites | Properties, Theorems, Proofs & Geometry Examples
Video 39: Topic 6.7 Constructing Squares, Rectangles, Rhombuses, Parallelograms, Trapezium, Isosceles Trapezium
Unit 7: Transformational Geometry
Video 40: Topic 7.1 Coordinate Geometry | Using Coordinates to Prove Geometric Relationships
Video 41: Topic 7.2 Translations of Geometric Shapes | Coordinate Geometry Transformations
Video 42: Topic 7.3 Reflections of Geometric Shapes | Coordinate Geometry Transformations
Video 43: Topic 7.4 Rotations of Geometric Shapes | Coordinate Geometry Transformations
Video 44: Topic 7.5 Symmetry | Line Symmetry, Rotational Symmetry & Transformations
Video 45: Topic 7.6 Compositions of Rigid Transformations | Translations, Reflections & Rotations
Video 46: Topic 7.7 Congruence Transformations | Rigid Transformations & Congruent Figures
Video 47: Topic 7.8 Dilations | Scale Factor, Enlargements & Reductions | Geometry Transformations
Video 48: Topic 7.9 Other Non-Rigid Transformations | Stretches, Compressions, Shears & More
Video 49: Topic 8.1 Similar Polygons | Proportions, Scale Factors & Geometry Applications
Video 50: Topic 8.2 Similarity Transformations | Dilations & Rigid Transformations Explained
Video 51: Topic 8.3 Proving Triangles Similar | AA, SAS & SSS Similarity Theorems
Video 52: Topic 8.4 Similarity in Right Triangles | Altitude-on-Hypotenuse Theorem & Similar Triangles
Video 53: Topic 8.5 Proportions in Triangles | Triangle Proportionality Theorems & Similarity
Unit 9: Right Triangles & Trigonometry
Video 54: Topic 9.1 The Pythagorean Theorem | Finding Missing Side Lengths in Right Triangles
Video 55: Topic 9.2 Special Right Triangles | 45-45-90 & 30-60-90 Triangles Explained
Video 56: Topic 9.3 Trigonometry in Right Triangles - Sine, Cosine, and Tangent - SOH, CAH - TOA
Video 57: Topic 9.4 Angles of Elevation & Depression | Right Triangle Applications & Trigonometry
Unit 10: Circle Equations & Circle Theorems
Video 58: Topic 10.1 Circles & Arcs | Circle Vocabulary, Arc Measures & Geometry Theorems
Video 59: Topic 10.2 Radian Measure | Converting Between Degrees & Radians
Video 60: Topic 10.3 Area of Sectors & Composite Figures | Arc Length, Sector Area & Geometry Applications.
Video 61: Topic 10.4A Writing & Graphing the Equation of a Circle | Tangent Lines to a Circle
Video 62: Topic 10.4B Circle Equations | Converting Standard Form to General Form.
Video 63: Topic 10.4C Circle Equations | Converting General Form to Standard Form by Completing the Square.
Video 64: Topic 10.6 Chords & Arcs | Circle Theorems, Angle Measures & Geometry Proofs
Video 65: Topic 10.7 Inscribed Angles | Central Angles | Intercepted Arcs, Circle Theorems & Geometry Proofs
Video 66: Topic 10.8 Angle Measures & Segment Lengths | Intersecting Chords, Secants & Tangents
Unit 11: Area, Surface Area, & Volume
Video 67: Topic 11.1 Perimeter & Area of Composite Figures | Geometry Applications & Problem Solving.
Video 68: Topic 11.2 Area of Regular Polygons | Apothem, Perimeter & Area Formula
Video 69: Topic 11.3 Perimeter & Area of Similar Figures | Scale Factors & Geometry Applications
Video 70: Topic 11.4 Trigonometry & Area | Area of Triangles Using Sine Formula
Video 71: Topic 11.5 3D Figures & Cross Sections | Prisms, Pyramids, Cylinders, Cones & Spheres
Video 72: Topic 11.6 Surface Area of Prisms & Cylinders | Lateral Area, Total Surface Area & Geometry Applications.
Video 73: Topic 11.7 Surface Area of Pyramids & Cones | Lateral Area, Total Surface Area & Geometry Applications.
Video 74: Topic 11.8 Volume of Prisms & Cylinders | Volume Formulas, Cavalieri's Principle & Applications.
Video 75: Topic 11.9 Volume of Pyramids & Cones | Volume Formulas, Cavalieri's Principle & Geometry Applications.
Video 76: Topic 11.10 Surface Area & Volume of Spheres | Sphere Formulas & Geometry Applications.
Video 77: Topic 11.11 Surface Areas & Volumes of Related Solids | Scale Factors & Similar Solids.
Unit 12: Probability & Statistics
Video 78: Topic 12.1 Experimental & Theoretical Probability | Probability Basics, Simulations & Applications
Video 79: Topic 12.2 Geometric Probability | Probability Using Length, Area & Volume
Video 80: Topic 12.3 Permutations & Combinations | Counting Principles, Factorials & Probability
Video 81: Topic 12.4 Compound Probability | Independent & Dependent Events | Mutually Exclusive & Non-Mutually Exclusive Events
Video 82: Topic 12.5 Conditional Probability with Frequency Tables | Two-Way Tables & Probability
Video 83: Topic 12.6 Conditional Probability Formulas | Two-Way Tables, Venn Diagrams & Bayes' Theorem
Video 84: Topic 12.7 Mean Absolute Deviation, Variance & Standard Deviation | 2 Methods Explained.
Assorted Advanced Concepts
Dive into a collection of advanced math concepts!
This series of videos covers a variety of challenging topics designed to deepen your understanding and sharpen your problem-solving skills. Whether you’re preparing for competitions, exams, or just love advanced math, these concepts will push your thinking and expand your toolkit. Ready to level up? Let’s get started!
Explore my playlist of nearly 1000 Math Olympiad problem videos, with new content added regularly. Dive in and challenge yourself!