GEOMETRY

Mr. P. Nelson

pnelson0502@yahoo.com

GENERAL COURSE DESCRIPTION

In geometry, students learn abstract and logical thinking through inductive and deductive reasoning. Students will use lines, planes, polygons, circles, and three-dimensional figures for representing and solving a variety of problems. Other areas of study include algebra, functions, and graphs.

The most important pages in your Geometry text:

• Postulates, Theorems, and Corollaries (Pages 692 - 700)

MATERIALS NEEDED

• Notebook paper

• Graph paper

• #2 pencils

• Scientific calculator

• Straight edge

• Compass

Useful Tools:

• https://www.desmos.com/geometry

• https://www.geogebra.org/geometry?lang=en

• Coordinate Grids

PROOF-WRITING

• Proofs Summary

• Online Proof Practice: http://feromax.com/cgi-bin/ProveIt.pl?task=getproofslist

LECTURE SUMMARIES

These are merely summaries of the topics covered in class. Additional topics, based on time and student interest, will likely be covered and will not be included here. By no means are these notes complete. Nor should these notes be used as a substitute for participating in class. Students should still take their own notes.

Chapter 1: Points, Lines, Planes, and Angles

• 1.2 Points, Lines, and Planes

• 1.3 Segments, Rays, and Distance

• 1.4 Angles

• 1.5 Postulates & Theorems Relating Points, Lines, and Planes

Chapter 2: Deductive Reasoning

• 2.1 If-Then Statements; Converses

• 2.2 Properties of Algebra

• 2.3 Proving Theorems

• 2.4 Special Pairs of Angles

• 2.5 Perpendicular Lines

• 2.6 Planning a Proof

Chapter 3: Parallel Lines and Planes

• 3.1 Definitions

• 3.2 Properties of Parallel Lines

• 3.3 Proving Lines Parallel

• 3.4 Angles of a Triangle

• 3.5 Angles of a Polygon

• 3.6 Inductive Reasoning

Chapter 4: Congruent Triangles

• 4.1 Congruent Figures

• 4.2 Some Ways to Prove Triangles Congruent

• 4.3 Using Congruent Triangles

• 4.4 The Isosceles Triangle Theorems

• 4.5 Other Methods of Proving Triangles Congruent

• 4.6 Using More Than 1 Pair of Congruent Triangles

• 4.7 Medians, Altitudes, and Perpendicular Bisectors

Chapter 5: Quadrilaterals

• 5.1 Properties of Parallelograms

• 5.2 Ways to Prove that Quadrilaterals are Parallelograms

• 5.3 Theorems Involving Parallel Lines

• 5.4 Special Parallelograms

• 5.5 Trapezoids

Chapter 6: Inequalities in Geometry

• 6.1 Inequalities

• 6.2 Inverses and Contrapositives

• 6.3 Indirect Proof

• 6.4 Inequalities for One Triangle

• 6.5 Inequalities for Two Triangles

Chapter 7: Similar Polygons

• 7.1 Ratio and Proportion

• 7.2 Properties of Proportions

• 7.3 Similar Polygons

• 7.4 A Postulate for Similar Triangles

• 7.5 Theorems for Similar Triangles

• 7.6 Proportional Lengths

Chapter 8: Right Triangles

• 8.1 Similarity in Right Triangles

• 8.2 The Pythagorean Theorem

• 8.3 The Converse of the Pythagorean Theorem

• 8.4 Special Right Triangles

• 8.5 The Tangent Ratio

• 8.6 The Sine and Cosine Ratios

• 8.7 Applications of Right Triangle Trigonometry

Chapter 9: Circles

• 9.1 Basic Terms

• 9.2 Tangents

• 9.3 Arcs and Central Angles

• 9.4 Arcs and Chords

• 9.5 Inscribed Angles

• 9.6 Other Angles

• 9.7 Circles and Lengths of Segments

Chapter 10: Constructions and Concurrent Lines

• 10.1, 10.2 Constructions

• 10.3 Concurrent Lines

Chapter 11: Areas of Plane Figures

• 11.1 Areas of Rectangles

• 11.2 Areas of Parallelograms, Triangles, and Rhombuses

• 11.3 Areas of Trapezoids

• 11.4 Areas of Regular Polygons

• 11.5 Circumferences and Areas of Circles

• 11.6 Arc Lengths and Areas of Sectors

• 11.7 Ratios of Areas

• 11.8 Geometric Probability

Chapter 12: Areas and Volumes of Solids

• 12.1 Prisms

• 12.2 Pyramids

• 12.3 Cylinders and Cones

• 12.4 Spheres

• 12.5 Areas and Volumes of Similar Solids

Chapter 13: Coordinate Geometry

• 13.1 The Distance Formula

• 13.2 Slope of a Line

• 13.3 Parallel and Perpendicular Lines

• 13.4 Vectors

• 13.5 The Midpoint Formula

• 13.6 Graphing Linear Equations

• 13.7 Writing Linear Equations

• 13.8 Organizing Coordinate Proofs

• 13.9 Coordinate Geometry Proofs

Chapter 14: Transformations

• 14.1 Mappings and Functions

• 14.2 Reflections

• 14.3 Translations and Glide Reflections

• 14.4 Rotations

• 14.5 Dilations

• 14.6 Composites of Mappings

• 14.7 Inverses and the Identity

• 14.8 Symmetry in the Plane and in Space

PLATONIC SOLIDS

• Polyhedra, Euler's Formula, and Platonic Solids

• Nets for Platonic Solids

Graphical Transformations

• G.1 & G.1 Worksheet

• G.2 & G.3: G.2 WS, G.3 WS

• G.4 & G.4 Worksheet

• G.5 & G.5 Worksheet

• G.6 & G.6 Worksheet

• G.7 & G.7 Worksheet

Chapter 4: Products and Factors of Polynomials

• 4.1 Polynomials

• 4.2 Using Laws of Exponents

• 4.3 Multiplying Polynomials

• 4.4 Using Prime Factorization

• 4.5 Factoring Polynomials

• 4.6 Factoring Quadratic Polynomials

• 4.7 Solving Polynomial Equations

• 4.8 Problem-Solving Using Polynomial Equations

• 4.9 Solving Polynomial Inequalities

Chapter 5: Rational Expressions

• 5.1 Quotients of Monomials

• 5.2 Zero and Negative Exponents

• 5.3 Scientific Notation

• 5.4 Rational Algebraic Expressions

• 5.5 Products and Quotients of Rational Expressions

• 5.6 Sums and Differences of Rational Expressions

• 5.7 Complex Fractions

• 5.8 Fractional Coefficients

• 5.9 Fractional Equations

Chapter 12: Triangle Trigonometry

• 12.1 Angles and Degree Measure

• 12.2 Trigonometric Functions of Acute Angles

• 12.3 Trigonometric Functions of General Angles

• 12.5 Solving Right Triangles

• 12.6 The Law of Cosines

• 12.7 The Law of Sines

• 12.8 Solving General Triangles

• 12.9 Areas of Triangles

Chapter 13: Trigonometric Graphs; Identities

• 13.1 Radian Measure

• 13.2 Circular Functions

• 13.3 Periodicity and Symmetry

• 13.4 Graphs of the Sine and Cosine

• 13.6 The Fundamental Identities

• 13.7 Trigonometric Addition Formulas

• The Unit Circle