# Geometry

Geometry Curriculum

1: Essentials of Geometry

Undefined Terms

Real Numbers and Properties

Lines and Line Segments

Angles

Preliminary Angles and Line Relationships

Triangles

2: Logic

Statements, Truth Values, and Negations

Compound Statements

Conditionals

Converses, Inverses, and Contrapositives

Biconditionals

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

Constructions

6: Transformations and the Coordinate Plane

Cartesian Coordinate System

Translations

Line Reflections and Symmetry

Point Reflections and Symmetry

Rotations

Dilations

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

Rectangles

Rhombus

Squares

Trapezoids

Kites

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

Cylinders

Pyramids

Cones

Spheres

12: Rations, Proportion, and Similarity

Ratio and Proportion

Proportions Involving Line Segments

Similar Polygons

Proving Triangles Similar

Dilations

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