AoPS Geometry
Lessons
Module 1: What's in a Name, Angles, and Congruent Triangles
Why names and symbols and Points, Lines, and Planes
Round and Round
Construction: Copy a Segment and the Burden of Proof
Definition of an Angle and Measuring Angles
Straight and Vertical Angles and Parallel Lines
Angles in a Triangle and Exterior Angles
Parallel Lines Revisited
Introduction to Congruent Triangles and SSS Congruence
SAS, ASA, and AAS Congruence
SSA Not-Necessarily Congruence and Isosceles and Equilateral Triangles
Construction: Equilateral and Perpendicular Bisector
Test 1 Review
Test 1
Module 2: Perimeter and Area, Similar Triangles, and Right Triangles
Perimeter and Area
Same Base and Altitude
Definition of Similarity
AA and SAS Similarity
SSS Similarity and Using Similarity in Problems
Construction: Angles and Parallels
Pythagorean Theorem and Two Special Right Triangles
Pythagorean Triples and Congruence and Similarity Revisited
Heron's Formula and Construction: Perpendicular Lines
Test 2 Review
Test 2
Module 3: Special Parts of a Triangle, Quadrilaterals, Polygons, and Geometric Inequalities
Bisectors and Perpendicular Bisectors of a Triangle
Angle Bisectors of a Triangle
Medians and Altitudes
Challenging Problems and Construction: Bisectors
Quadrilateral Baiscs and Trapezoids
Parallelograms and Rhombi
Rectangles and Squares
If and Only If and Quadrilateral Problems
Introduction to Polygons and Angles in a Polygon
Polygon Area and Polygon Problems
Construction: Regular Polygons
Sides and Angles of a Triangle and Pythagoras - Not Just for Right Triangles
The Triangle Inequality
Test 3 Review
Test 3
Midterm Review
Midterm
Module 4: Circles, Angles, and Power of a Point
Arc Measure, Arc Length, and Circumference
Area
Funky Areas
Inscribed Angles
Angles Inside and Outside Circles
Tangents
Problems
Construction: Tangents
Definition of Power of a Point
Power of a Point Problems
Test 4 Review
Test 4
Module 5: Three-Dimensional Geometry, Curved Surfaces, and The More Things Change
Planes
Prisms
Pyramics
Regular Polyhedra
Cylinders
Cones
Spheres
Problems
Translations
Rotations
Reflections
Dilation
Changing the Question
Construction: Transformations
Test 5 Review
Test 5
Module 6: Analytic Geometry, Introduction to Trigonometry, and Problem Solving Strategies in Geometry
Lines
Circles
Basic Analytic Geometry Problems
Proofs with Analytic Geometry
Distance Between a Point and a Line
Advanced Analytic Geometry Problems
Trigonometry and Right Triangles
Not Just for Right Triangles
Law of Sines and Law of Cosines
The Extra Line
Assigning Variables
Proofs
Test 6 Review
Test 6
Final Exam Review
Final Exam
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