Discipline: Mathematics
Originator: Kenneth Cramm

Riverside Community College District
Integrated Course Outline of Record

Mathematics 53
MAT-53 : College Geometry
College:
Lecture Hours: 54.000
Outside-of-Class Hours: 108.000
Units: 3.00
Grading Methods: Pass/No Pass
Letter Grade
Course Description
Prerequisite: MAT-52 or qualifying placement.
Course Credit Recommendation: Degree Credit

A course covering the study of plane geometry and three dimensional figures. These topics include angles, triangles, quadrilaterals, circles and solids, their formulas for measuring such figures, including perimeter, area and volume. Students create proofs of geometric concepts using postulates and theorems associated with geometric objects and their characteristics. 54 hours lecture.
Short Description for Class Schedule
A course in the study of 2 and 3 dimensional geometry.
Entrance Skills:
Before entering the course, students should be able to demonstrate the following skills:
  1. Simplify algebraic expressions, and factor polynomials, by using correct mathematical symbols and logic.
    • MAT-52 - Simplify algebraic expressions using correct mathematical symbols and language.
    • MAT-52 - Factor polynomials.
  2. Identify and apply appropriate methods to solve linear, quadratic, rational, and radical equations.
    • MAT-52 - Identify and apply appropriate methods to solve linear, quadratic, rational, and radical equations.
  3. Solve applications that require writing and solving equations. Communicate solution in the context of the problem.
    • MAT-52 - Solve applications that require writing and solving equations. Communicate solution in the context of the problem.
Course Objectives:
Upon successful completion of the course, students should be able to demonstrate the following activities:
  1. Write a 2-column proof using logic and reasoning.
  2. Calculate segment lengths and angle measures using geometric structures.
  3. Compare unequal measures within geometric shapes.
  4. Use altitude and other line segments to calculate perimeter, area, and volume.
  5. Use the Pythagorean Theorem and special triangle properties to discover unknown quantities.
  6. Utilize a variety of line segments with circles to calculate angle and length.
  7. Apply geometric data to generate the surface area and volume of any geometric structure.
Student Learning Outcomes:
Upon successful completion of the course, students should be able to demonstrate the following skills:
  1. Compose written proofs of geometric statements.
    • Critical Thinking: Students will be able to demonstrate higher-order thinking skills about issues, problems, and explanations for which multiple solutions are possible. Students will be able to explore problems and, where possible, solve them. Students will be able to develop, test, and evaluate rival hypotheses. Students will be able to construct sound arguments and evaluate the arguments of others.
  2. Solve problems involving angles and transversals.
    • Communication Skills: Students will be able to communicate effectively in diverse situations. They will be able to create, express, and interpret meaning in oral, visual, and written forms. They will also be able to demonstrate quantitative literacy and the ability to use graphical, symbolic, and numerical methods to analyze, organize, and interpret data.
  3. Solve applications using the Pythagorean Theorem, special right triangles, and the components of regular and non-regular polygons.
  4. Solve circle problems using area and angles information.
  5. Use geometric formulas for area and volume to calculate exact and approximate values of area, volume, or a missing length.
    • Critical Thinking: Students will be able to demonstrate higher-order thinking skills about issues, problems, and explanations for which multiple solutions are possible. Students will be able to explore problems and, where possible, solve them. Students will be able to develop, test, and evaluate rival hypotheses. Students will be able to construct sound arguments and evaluate the arguments of others.
Course Content:
  1. Proofs
    1. Logic
    2. Reasoning
  2. Lines and angle relationships 
    1. Definitions, postulates, and theorems
    2. Parallel, perpendicular, and intersecting lines
    3. Segment measurements
  3. Triangles 
    1. Congruent triangles and corresponding parts of congruent triangles
    2. Inequalities in triangles
  4. Polygon Properties 
    1. Use of altitude and like line segments
    2. Perimeter and area
  5. Similar Polygon 
    1. Ratios, rates, and proportions
    2. Similar triangles
    3. Proofs of similar triangles and polygons
    4. The Pythagorean Theorem
    5. Segments divided proportionally
    6. Special right triangles
  6. Circles 
    1. Related segments and angles
    2. Inequalities of chords and angles
    3. Circumference and area
  7. Surface and Solids 
    1. Polygons and polyhedrons
    2. Spheres
    3. Surface area and volume

 

Methods of Instruction:
Methods of instruction used to achieve student learning outcomes may include, but are not limited to, the following activities:
  • Present class lectures/discussions/demonstrations in order to familiarize students with the definitions and theorems of elements of geometry.
  • Create activities in order to provide an opportunity for students to the practice solving triangle problems with group interaction and support.
  • Use computer-assisted or web-enhanced instruction for, but not limited to, understanding surface area and volume of geometric objects.
Methods of Evaluation:
Students will be evaluated for progress in and/or mastery of student learning outcomes using methods of evaluation which may include, but are not limited to, the following activities:
  • Oral reports or presentations aimed to demonstrate knowledge of geometric principles.
  • Homework and quizzes designed to assess the progress and ability to recall algebraic concepts to formulate solutions to geometric concepts.
  • Group and individual projects designed to ensure progress in mastering the fundamental properties of geometry.
  • Midterm and final examination designed to assess students’ mastery and ability to prove, organize, and present complete solutions to geometric concepts

 

Sample Assignments:
Outside-of-Class Reading Assignments
  • Reading of the textbook, handouts, or lecture notes on topics that include, and are not limited to, circumference, logical reasoning, and using the Pythagorean Theorem.
Outside-of-Class Writing Assignments
  • Create vocabulary list from each chapter.
  • Practice using the symbols of Geometry to replace more common words.
  • For example, use ~ to replace the words "is similar to".
Other Outside-of-Class Assignments
  • Review study guides, homework problems, and topic related videos on concepts related to, but not limited to, the use of algebra to find angle and line segment measures.
Course Materials:
All materials used in this course will be periodically reviewed to ensure that they are appropriate for college level instruction. Possible texts include the following:
  • Alexander & Koeberlein. Elementary Geometry for College Students. 6th Brooks/Cole Cengage Learning, 2015.
  • Musser, Trimpe, Maurer. College Geometry. 2nd Pearson, 2008.
Codes/Dates:
CB03 TOP Code: 1701.00 - Mathematics, General
CB05 MOV Transfer Status: Non-Transferable (C)
CB05 NOR Transfer Status: Non-Transferable (C)
CB05 RIV Transfer Status: Non-Transferable (C)
Board of Trustees Approval Date: 01/15/2019
COR Rev Date: 01/15/2019