## Table of Contents

**1. Foundations of Geometry.**

Inductive and Deductive Reasoning.

Points, Lines and Planes.

Segments, Rays, and Angles.

Introduction to Deductive Proofs.

Formalizing Geometric Proofs.

Constructions Involving Lines and Angles.

**2. Triangles.**

Classifying Triangles.

Congruent Triangles.

Proofs Involving Congruence.

Isosceles Triangles, Medians, and Altitudes.

Proving Right Triangles Congruent.

Constructions Involving Triangles.

**3. Parallel Lines and Polygons.**

Indirect Proof and the Parallel Postulate.

Parallel Lines.

Polygons and Angles.

More Congruent Triangles.

**4. Quadrilaterals.**

Parallelograms.

Rhombus and Kite.

Rectangles and Squares.

Trapezoids.

**5. Similar Polygons and the Pythagorean Theorem.**

Ratio and Proportion.

Similar Polygons.

Properties of Right Triangles.

Pythagorean Theorem.

Inequalities Involving Triangles.

**6. Circles.**

Circles and Arcs.

Chords and Secants.

Tangents.

Circles and Regular Polygons.

Inequalities Involving Circles.

**7. Areas of Polygons and Circles.**

Areas of Quadrilaterals.

Circumference and Area of a Circle.

Area and Arc Length of a Sector.

Area of Regular Polygons.

**8. Solid Geometry.**

Planes and Polyhedrons.

Prisms.

Pyramids.

Cylinders and Cones.

Spheres and Composite Figures.

**9. Analytic Geometry and Locus of Points.**

The Cartesian Coordinate System.

Slope, Distance and Midpoint Formulas.

Proofs Involving Polygons.

Locus and Basic Theorems.

Triangle Concurrency Theorems.

**10. Introduction to Trigonometry.**

Sine and Cosine Ratio.

Tangent Ratio.

Solving Right Triangles.

Applications Involving Right Triangles.

### Additional Course Materials

Essentials of Geometry, Books a la Carte Edition, 2nd Edition

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