Essentials of Geometry for College Students

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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.