20804200Principles of Geometry
Course Information
Description
This is an introductory college level course that provides a foundation in geometry necessary for the study of analytic geometry, trigonometry, or calculus. The class covers the facts of geometry, cultivates geometric intuition, and fosters the practice of deductive reasoning. Prerequisite: Algebra Concepts, 10-804-140 with a grade of C or better or appropriate placement score.
Total Credits
3
Course Competencies
  1. Identify the basic objects and relations of geometry and measures angles and segments
    Assessment Strategies
    by a satisfactory score on all tests, quizzes, or graded assignments incorporating this competency
    Criteria
    you identify points, lines, line segments and angles, and labels them appropriately
    you measure segments with a ruler and angles with a protractor
    you demonstrate understanding of congruence of segments and angles
    you demonstrate skill in completing simple proofs
    you show how to use the basic geometric constructions

  2. Solve problems involving triangles
    Assessment Strategies
    by a satisfactory score on all tests, quizzes, or graded assignments incorporating this competency
    Criteria
    you identify the different types of triangles
    you identify congruent triangles
    you solve problems concerning angles by using the fact about the sum of the measures of the angles
    you use the theorems on congruence (SSS, SAS, ASA, HL) to prove other theorems and solve problems
    you analyze components of problems using the theorems and definitions to solve progressively more complex problems

  3. Use parallel lines and figures with parallel lines
    Assessment Strategies
    by a satisfactory score on all tests, quizzes, or graded assignments incorporating this competency
    Criteria
    you identify parallel, corresponding angles, alternate interior angles, interior angles
    you use the axioms and theorems concerning parallel lines
    you identify quadrilaterals with parallel lines: trapezoid, parallelogram, rhombus, rectangle, square
    you apply the various properties of such quadrilaterals to solving problems which combine one or more such figures
    you demonstrate skill in constructions using parallel lines
    you identify the role of Euclid's 5th Postulate in the evolution of modern mathematics
    you recognize the impossibility of certain constructions
    you apply the process for solving progressively more complex problems according to the problem solving criteria

  4. Solve problems using the Pythagorean Theorem and its converse
    Assessment Strategies
    by a satisfactory score on all tests, quizzes, or graded assignments incorporating this competency
    Criteria
    you summarize the Pythagorean Theorem and its converse
    you compute a missing side of a right triangle
    you show that 3 given sides form a right triangle by using the converse of the Pythagorean Theorem
    you construct Pythagorean Triples using any pair of generators and demonstrate understanding of the influence in the development of modern abstract mathematics culminating in Andrew Wiles proof of Fermat's Last Theorem in 1994
    you apply skill to applied geometric problems
    you apply the process for solving progressively more complex problems according to the problem solving criteria

  5. Compute perimeters and areas of geometric shapes
    Assessment Strategies
    by a satisfactory score on all tests, quizzes, or graded assignments incorporating this competency
    Criteria
    you illustrate the importance of the assumption that congruent polygons have equal areas
    you calculate the area of non-overlapping unit squares covering a figure
    you distinguish rectangles, squares, parallelograms and triangles so that the appropriate formulas for perimeter and area can be used
    you apply the correct formulas to models of the geometric objects
    you apply the process for solving progressively more complex problems according to the problem solving criteria

  6. Solve problems involving similar triangles and other similar figures
    Assessment Strategies
    by a satisfactory score on all tests, quizzes, or graded assignments incorporating this competency
    Criteria
    you describe the concept of similar figures and points out examples in scale drawings and maps
    you identify when two triangles are similar using the AA fact
    you solve for missing parts of pairs of similar triangles
    you apply skill to dissecting and analyzing complex problems into component pairs of similar triangles

  7. Solve problems using right triangle trigonometry (optional)
    Assessment Strategies
    by a satisfactory score on all tests, quizzes, or graded assignments incorporating this competency
    Criteria
    you summarize the definition of sin, cos, tan
    you calculate the sin, cos, tan of any angle in degrees using a scientific calculator
    you use sine, cosine, and tangent ratios to compute sides and/ or angles of right triangles
    you solve for missing parts of right triangles which model real world problems
    you apply the process for solving problems according to the problem solving criteria

  8. Solve problems involving circles
    Assessment Strategies
    by a satisfactory score on all tests, quizzes, or graded assignments incorporating this competency
    Criteria
    you identify circles and the various parts: radius, diameter, chord, central angle
    you use the definition of arc measure and the formula for the measure of an inscribed angle to solve for angles formed by radii, diameters and chords
    you use the fact that a tangent line and the radius drawn to the point of tangency are perpendicular
    you apply skill to applied problems modeled by circles and lines
    you apply the process for solving progressively more complex problems according to the problem solving criteria

  9. Solve solid geometry problems involving solids in space
    Assessment Strategies
    by a satisfactory score on all tests, quizzes, or graded assignments incorporating this competency
    Criteria
    you identify relationships between lines and planes in space
    you distinguish the different solids (polyhedra, prisms, rectangular solids, pyramids, tetrahedra, cylinders, cones, and spheres
    you calculate volumes and surface areas of the different solids usings appropriate formulas
    you use the extension of the Pythagorean Theorem in space
    you extend the facts of plane geometry to the parts of solid figures
    you apply the process for solving progressively more complex problems according to the problem solving criteria