Download Seminar Geometry

Radnor High School
Course Syllabus
Seminar Geometry
0429
I. Course Description
This course is a challenging, rigorous, proof-based approach to Geometry. Students in Seminar Geometry
analyze geometric figures using deductive reasoning, make conjectures and formulate hypotheses, draw
conclusions and make connections with other mathematical concepts, and model situations geometrically as a
problem solving strategy. Algebraic and geometric skills are integrated throughout the curriculum.
II. Materials & Equipment
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Geometry for Enjoyment and Challenge; McDougal, Littell; 1991
Non-graphing, scientific calculator
Geometer, compass, and straight edge
Three – Ring Binder Notebook
Water-Based Overhead Marker
III. Course Goals & Objectives
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To develop the ability to think mathematically.
To enhance problem solving ability.
To use technology appropriately.
To present a mathematical model of the physical world.
To provide experience in solving geometry problems by deductive methods, direct or indirect.
To supplement the basics of plane geometry with a foundation in space geometry, coordinate geometry
and transformational geometry.
To see the interrelationship of geometry to other fields of mathematics and relevant life situations.
To challenge and utilize the inquisitive and logical minds of the accelerated math students.
To foster specific problem solving strategies in an overall problem solving approach to mathematics.
IV. Course Topics (Summary Outline)
I.
INTRODUCTION TO GEOMETRY
 Introductory Terminology
 Measurement of Segments and
Angles
 Collinearity, Betweenness, and
Assumptions
 Beginning Proofs
 Division of Segments and Angles
 Paragraph Proofs
 Deductive Structure
 Statements of Logic
 Probability
Revised 05/17/2011
II.
BASIC CONCEPTS AND PROOFS
 Perpendicularity
 Complementary and
Supplementary Angles
 Drawing Conclusions
 Congruent Supplements and
Complements
 Addition and Subtraction
Properties
 Multiplication and Division
Properties
 Transitive and Substitution
Properties
 Vertical Angles
III.
CONGRUENT TRIANGLES
 Congruent Figures
 Methods to Prove Triangles
Congruent
 CPCTC and beyond
 Circles
 Overlapping Triangles
 Types of Triangles
 Angle –Side Theorems
IV.
LINES IN THE PLANE
 Detours and Midpoints
 The Case of the Missing Diagram
 A Right-Angle Theorem
 The Equidistance Theorems
 Introduction to Parallel Lines
 Slope
V.
PARALLEL LINES AND RELATED
FIGURES
 Indirect Proof
 Proving That Lines Are Parallel
 Congruent Angles Associated with
Parallel Lines
 Four-Sided Polygons
 Properties of Quadrilaterals
 Proving That a Quadrilateral is a
Parallelogram
 Proving That Figures Are Special
Quadrilaterals
VI.
LINES AND PLANES IN SPACE
 Relating Lines to Planes
 Perpendicularity of a Line and a
Plane
 Basic Facts about Parallel Planes
VII.
POLYGONS
 Triangle Application Theorems
 Two Proof- Oriented Triangle
Theorems
 Formulas Involving Polygons
 Regular Polygons
VIII.
SIMILAR POLYGONS
 Ratio and Proportion
 Similarity
 Proving Triangles Similar
 Congruence and Proportions in
Similar Triangles
 Three Theorems Involving
Proportions
Revised 05/17/2011
IX.
THE PYTHAGOREAN THEOREM
 Review of Radicals and Quadratic
Equations
 Introduction to Circles
 Altitude-on-Hypotenuse Theorems
 Pythagorean Theorem
 The Distance Formula
 Pythagorean Triples
 Special Right Triangles
 The Pythagorean Theorem and
Space Figures
 Right Triangle Trigonometry
X.
CIRCLES
 The Circle
 Congruent Chords
 Arcs of a Circle
 Secants and Tangents
 Angles Related to a Circle
 Inscribed and Circumscribed
Polygons
 The Power Theorems
 Circumference and Arc Length
XI.
AREA
 Area of Parallelograms, Squares,
Rectangles and Triangles
 The Area of a Trapezoid
 Area of Kites and Related Figures
 Area of Regular Polygons
 Areas of Circles, Sectors, and
Segments
 Ratios of Areas
 Hero’s and Brahmagupta’s
Formulas
XII.
SURFACE AREA AND VOLUME
 Surface Areas of Prisms
 Surface Area of Pyramids
 Surface Areas of Circular Solids
 Volumes of Prisms and Cylinders
 Volumes of Pyramids and Cones
 Volumes of Spheres
 Ratios of Volumes of Similar Solids
Continued on the next page:
XIII.
COORDINATE GEOMETRY
EXTENDED
 Graphing Equations
 Equations of Lines
 Systems of Equations
 Graphing Inequalities
 Three-Dimensional Graphing and
Reflections
 Equations of a Circle
 Coordinate-Geometry Practice
XIV.
LOCUS AND CONSTRUCTIONS
 Locus
 Compound Locus (if time permits)
 The Concurrence Theorems
 Basic Constructions
 Applications of the Basic
Constructions
 Triangle Constructions
XV.
INEQUALITIES
 Number Properties
 Inequalities in a Triangle
 The Hinge Theorems
XVI.
ENRICHMANT TOPICS (Independent
study for students participating in math
team, and/or mathematics
competitions.)
 The Point-Line Distance Formula
 Two Other Useful Formulas
 Stewart’s Theorem
 Ptolemy’s Theorem
 Mass Points
 Inradius and Circumradius
Formulas
 Formulas for You to Develop
Note: Algebra Reviews will also be assigned on a
regular basis throughout the year in order for the
students to maintain and extend their knowledge of
Algebra.
V. Assignments & Grading
Assignment sheets will be distributed periodically throughout the school year. Homework will
be assigned on a daily basis. Grades will be based on quizzes and tests. In addition, teachers
may use homework, group activities, and/or projects for grading purposes. All students will take
departmental midyear and final exams. The Radnor High School grading system and scale will
be used to determine letter grades.
Revised 05/17/2011