Mathematics » Geometry


Geometry Curriculum
1: Essentials of Geometry
Undefined Terms
Real Numbers and Properties
Lines and Line Segments
Preliminary Angles and Line Relationships

2: Logic
Statements, Truth Values, and Negations
Compound Statements
Converses, Inverses, and Contrapositives
Laws of Logic
Proof in Logic

3: Introduction to Geometric Proof
Inductive Reasoning
Definitions and Logic
Deductive Reasoning
Indirect Proof
Postulates, Theorems, and Proof
Remaining Postulates of Equality

4:Congruence of Lines, Angles, and Triangles
Setting Up A Valid Proof
Proving Theorems About Angles
Congruent Polygons

5: Congruence Based on Triangles
Line Segments Associated with Triangles
Using Congruent Triangles to Prove Line Segments
Isosceles and Equilateral Triangles
Working with Two Pairs of Congruent Triangles
Proving Overlapping Triangles Congruent
Perpendicular Bisectors of a Line Segment

6: Transformations and the Coordinate Plane
Cartesian Coordinate System
Line Reflections and Symmetry
Point Reflections and Symmetry
Properties Under Transformations
Composition of Transformations

7: Polygon Sides and Angles
Basic Inequality Postulates
The Triangle Inequality Theorem
The Exterior Angles of a Triangle
Inequalities Involving Sides and Angles of Triangles

8: Slopes and Equations of Lines
The Slope of a Line
The Equation of a Line
The Slopes of Parallel and Perpendicular Lines
The Midpoint of a Line Segment
Coordinate Plane
Concurrence of the Altitudes of a Triangle

9: Parallel Lines
Proving Lines Perpendicular
Proving Lines Parallel
Properties of Parallel Lines
Parallel Lines in the Coordinate Plane
The Sum of the Measures Congruent by Angle, Angle, Side
The Converse of the Isosceles Triangle Theorem
Proving Right Triangles Congruent by a Hypotenuse-Leg
Interior and Exterior Angles of Polygons

10: Quadrilaterals
The General Quadrilateral
The Parallelogram
Proving That A Quadrilateral is a Parallelogram
Areas of Polygons

11: Geometry of Three Dimensions
Points, Lines, and Planes
Perpendicular Lines, Planes, and Dihedral Angles
Parallel Lines and Planes
Surface Area of a Prism
Symmetry Planes
Volume of a Prism

12: Rations, Proportion, and Similarity
Ratio and Proportion
Proportions Involving Line Segments
Similar Polygons
Proving Triangles Similar
Proving Proportional Relationships
Using Similar-Triangles to Prove Proportions
Proportions in a Right Triangle
Pythagorean Theorem and Special Triangles
Perimeters, Areas. And Volumes of Similar Figures

13: Geometry of the Circle
Arcs and Angles
Arcs and Chords
Inscribed Angles and their Measure
Tangents and Secants
Angles Formed by Tangents, Chords, and Secants
Measures of Tangent Segments, Chords, and Secant Segments
Circle Proofs
Circles in the Coordinate Plane
Tangents, Secants, and the Circle in the Coordinate Plane

14: Locus and Constructions
Basic Constructions
Concurrent Lines and Points of Concurrency
The Meaning of Locus
Six Fundamental Loci and the Coordinate Plane
Compound Locus and the Coordinate
Locus of Points Equidistant from a Point and a Line
Solving Other Linear-Quadratic and Quadratic-Quadratic Systems