TRI-COUNTY TECHNICAL COLLEGE

Pendleton, South Carolina

COURSE SYLLABUS

Course Prefix & Number:    MAT 168                        

Course Title:                        Geometry and Trigonometry

Class  Hours                           Lab Hours                              Credits

Per week:  3                           Per Week:  0                         Awarded:  3

Catalog Description:   This course includes the following topics: points, lines, angles, and  angle measure; triangles; polygons; circles; geometric solids; trigonometric solutions of triangles; graph of the sine function; and vectors.

Entry Level Skills:     The student should be able to perform binary operations with whole numbers, fractions, decimals, signed numbers, solve linear equations, graph in the rectangular coordinate system, evaluate expressions with positive and negative, and utilize exponents.

Pre-requisites: MAT 101

Co-requisites: None

Text(s)/Required Materials: Alexander, P. and G. Koeberlein.  Elementary Geometry for College Students.    Houghton Mifflin, 2007.

Equipment: Scientific calculator, compass, protractor and straight edge.

Course Competencies and Objectives/Major Course Topics:

Unit 1: Introduction to Geometry

Upon completion of this unit (Sections 1.1-1.7: 2.1-2.6), the student should be able:

  1. To develop skills in working with geometric models.
  2. To explore basic geometric figures and to develop skills in inductive reasoning.
  3. To develop skills in using inductive and deductive reasoning.
  4. To become familiar with angles and their measurements and explore right angles and perpendicular lines.
  5. To investigate congruence and construction techniques.
  6. To identify the characteristics of true and false conditional statements.
  7. To write the converse, inverse, and contrapositive of a conditional statement, and to understand the relationships among the truth values of these statements.
  8. To apply given information and rules of logic to reach valid conclusions.
  9. To learn which geometric terms are undefined and to begin writing definitions.
  10. To classify different types of angles.
  11. To discover the Angle – Additive Postulate.
  12. To develop definitions and theorems about special angle pairs.
  13. To discover that vertical angles are congruent.
  14. To determine the angles created by two lines cut by a transversal.
  15. To see relationships among angles formed when a transversal intersects two parallel lines.
  16. To find ways to use angles formed by transversals to prove lines parallel.
  17. To identify relationships among angles formed by parallel lines and transversals.

Unit 2: Triangles

Upon completion of this unit (Sections 3.1-3.5: 5.1-5.6), the student should be able:

  1. To discover that the sum of the measures of the interior angles of a triangle is 180.
  2. To discover that the measure of an exterior angle is equal to the sum of the measures of its remote interior angles.
  3. To identify corresponding parts of congruent triangles.
  4. To apply SSS, SAS, ASA, and AAS to show that triangles are congruent.
  5. To investigate different ways to organize proofs.
  6. To show that sides or angles are congruent because they are corresponding parts of congruent triangles.
  7. To apply the Isosceles Triangle Theorem and its converse.
  8. To apply the Hypotenuse-Leg Congruence Theorem.
  9. To investigate special lines in triangles and to find that the centroid of a triangle is its center of balance.
  10. To discover that the longest side of a triangle is opposite the largest angle and vice versa.
  11. To discover and apply the Triangle Inequality Theorem.
  12. To explore scale factors and develop a formal definition of similar figures.
  13. To apply proportions to find side lengths of similar figures.
  14. To discover the AA similarity postulate and use it to solve real-world problems.
  15. To discover SAS and SSS similarity theorems and use them to solve real-world problems.

Unit 3: Polygons and Circles

Upon completion of this unit (Sections 4.1-4.3: 7.1-7.5), the student should be able:

  1. To see relationships among different quadrilaterals, and to discover that the sum of their interior angles is 360.
  2. To discover and confirm properties of parallelograms.
  3. To investigate ways to show that quadrilaterals are parallelograms.
  4. To investigate and confirm properties of diagonals of rectangles, rhombuses, and squares.
  5. To discover and use the area formula for a regular polygon and to find the measures of one interior and one exterior angle of a regular polygon.
  6. To develop and use a formula for the area of a circle.
  7. To develop and use a formula for the circumference of a circle.

Unit 4: Circles, Surfaces, and Solids

Upon completion of this unit (Sections 6.1-6.4: 8.1-8.4), the student should be able:

  1. To investigate circles and inscribed and circumscribed figures.
  2. To discover that a tangent line is perpendicular to the radius of a circle at the point of tangency and other theorems about tangent lines and segments.
  3. To explore central angles and measurements of major and minor areas.
  4. To apply proportional thinking to find areas of sectors and length of arcs.
  5. To explore relationships between chords and radii.
  6. To discover that the measure of an inscribed angle is one-half the measure of its intercepted arc.
  7. To explore relationships among arcs and angles whose vertices are inside, on, and outside the circle.
  8. To discover and use formulas for lateral and surface areas of right prisms.
  9. To discover and use formulas for lateral and surface areas of regular pyramids.
  10. To discover and use a formula for lateral and surface areas of right cylinders and cones.
  11. To explore the concept of volume, and to discover and use a formula for the volume of a prism.
  12. To discover and use a formula for the volume of a pyramid.
  13. To discover and use the formulas for the volumes of cylinders and cones.
  14. To discover and use formulas for the surface area and volume of a sphere.
  15. To discover that the ratio of the surface areas of two similar solids is the square of their similarity ratio.
  16. To discover that the ratio of the volume of two similar solids is the cube of their similarity ratios.
  17. To become familiar with the Platonic solids.

Unit 5: Trigonometry and Analytic Geometry

Upon completion of this unit (Sections 10.1-10.4: 9.1-9.5), the student should be able:

  1. To apply trigonometry to solve for a side length in a right triangle.
  2. To apply angles of elevation and depression to solve real-world problems and use trigonometry to solve for an angle measure.
  3. To find the length of segments on a number line and a coordinate plane.
  4. To apply coordinate geometry in proofs about quadrilaterals.

Grade Calculation Method:      

Final Course Grade                                       

Units(including homework, projects, and tests  83.3%         

Final Exam                                                                     16.7%                                                                                                                                                                           100.0% 

Prepared by__Joseph Stearns_____             Date written or revised:_September 7, 2006___