AOPS

Introduction to Geometry

 Syllabus

Syllabus

1 What's in a Name

 1.1 Why Names and Symbols?

 1.2 Points Lines and Planes

 1.3 Round and Round

 1.4 Construction: Copy a Segment

 1.5 The Burden of Proof

 1.6 Summary


2 Angles

 2.1 What is an Angle?

 2.2 Measuring Angles

 2.3 Straight and Vertical Angles

 2.4 Parallel Lines

 2.5 Angles in a Triangle

 2.6 Exterior Angles

 2.7 Paralle! Lines Revisited

 2.8 Summary


3 Congruent Triangles

 3.1 Introduction

 3.2 SSS Congruence

 3.3 SAS Congruence

 3.4 ASA and AAS Congruence

 3.5 SSA Not-Necessarily Congruence

 3.6 Isosceles and Equilateral Triangles

 3.7 Construction: Equilateral Trangle and Perpendicular Bisector

 3.8 Summary


4 Perimeter and Area

 4.1 Perimeter

 4.2 Area

 4.3 Same Base/Same Altitude

 4.4 Summary


5 Similar Triangles

 5.1 What is Similarity?

 5.2 AA Similarity

 5.3 SAS Similanity

 5.4 SSS Similarity

 5.5 Using Similarity in Problems

 5.6 Constructlon: Angles and Parallels

 5.7 Summary


6 Right Triangles

 6.1 Pythagorean Theorem

 6.2 Two Special Right Triangles

 6.3 Pythagorean Triples

 6.4 Congruence and Similarity Revisited

 6.5 Heron's Formula

 6.6 Construction: Perpendicular Lines

 6.7 Summary


7 Special Parts of a Triangle

 7.1 Bisectors

 7.2 Perpendicular Bisectors of a Triangle

 7.3 Angle Bisectors of a Triangle

 7.4 Medians

 7.5 Altitudes

 7.6 Challenging Problems

 7.7 Construction: Bisectors

 7.8 Summary


8 Quadrilaterals

 8.1 Quadrilateral Basics

 8.2 Trapezoids

 8.3 Parallelograms

 8.4 Rhombl

 8.5 Rectangies

 8.6 Squares

 8.7 lf and Only if

 8.8 Quadrilateral Problems

 8.9 Summary


9 Polygons

 9.1 introduction to Polygons

 9.2 Angles in a Polygon

 9.3 Polygon Area

 9.4 Polygon Problems

 9.5 Construction: Regular Polygons

 9.6 Summary


10 Geometric inequalities

 10.1 Sides and Angles of a Triangle

 10.2 Pythagoras - Not Just For Right Triangles?

 10.3 The riangle tnequality

 10.4 Summary


11 Circles

 11.1 Arc Measure, Arc Length, and Circumference

 11.2 Area

 11.3 Funky Aress

 11.4 Summary


12 Circles and Angles

 12.1 Inscribed Angles

 12.2 Angles inside and Outside Circles

 12.3 Tangents

 12.4 Problems

 12.5 Construction; Tangents

 12.6 Summary


13 Power of a Point

 13.1 What is Power of a Point?

 13.2 Power of a Paint Problems

 13.3 Summary


14 Three-Dimensional Geometry

 14.1 Planes

 14.2 Prisms

 14.3 Pyramids

 14.4 Regular Polyhedra

 14.5 Summary


15 Curved Surfaces

 15.1 Cylinders

 15.2 Cones

 15.3 Spheres

 15.4 Problems

 15.5 Summary


16 The More Things Change

 16.1 Transiations

 16.2 Rotations

 16.3 Reflections

 16.4 Dilation

 16.5 Changing the Question

 16.6 Construction: Transformations

 16.7 Summary


17 Analytic Geometry

 17.1 Lines

 17.2 Circles

 17.3 Basic Analytic Ceometry Problems

 17.4 Proofs with Analytic Geometry

 17.5 Distance Between a Point and a Line

 17.6 Advanced Analytic Geometry Problems

 17.7 Summary


18 Introduction to Trigonometry

 18.1 Trigonometry and Right Triangles

 18.2 Not Just For Right Triangles

 18.3 Law of Sines and Law of Cosines

 18.4 Summary


19 Problem Solving Strategies in Geometry

 19.1 The Extra Line

 19.2 Assigning Variables

 19.3 Proofs

 19.4 Summary