PLANE GEOMETRY 0000B ( Official )
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PLANE GEOMETRY 0000B ( Official )
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PLANE GEOMETRY 0000B ( Official )

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1. Division:

  Sciences & Mathematics

2. Course Discipline:


3. Course Number:


4. Course Title:


5. First semester this new version/new course will be offered: Fall 2013




General Course Information


1. Units: 4.0                 Variable units N/A

2. This Course is:

Degree-Applicable Credit - Non-Transferable


3A.  Cross-List: 


3B.  Formerly:




Course Format and Duration


4. Standard Term Hrs per Wk


5. Standard Term Total Semester Hrs
















By Arrangement:



By Arrangement:


Total Hrs per Wk



Total Hrs



6. Minimum hours per week of independent work done outside of class:    8


Course Preparation – (Supplemental form B required)


7a. Prerequisite(s): (Course and/or other preparation/experience that is REQUIRED to be completed previous to enrollment in this course.)

Completion of MATH A with grade of "C" or better, or placement by matriculation assessment process


7b. Co-requisite(s):  (Courses and/or other preparation that is REQUIRED to be taken concurrently with this course.)


7c. Advisory: (Minimum preparation RECOMMENDED in order to be successful in this course.  Also known as “Course Advisory”.)




Catalog Description And Other Catalog Information


8. Repeatability:

Not Repeatable

Please Note: 8. (Repeatability) does not refer to repeating courses because of substandard grades or a lapse of time since the student took the course. A course may be repeated only if the course content differs each time it is offered and the student who repeats it is gaining an expanded educational experience as stipulated in Title 5.


Skills or proficiencies are enhanced by supervised repetition and practice within class periods.

Active participatory experience in individual study or group assignments is the basic means by which course objectives are attained.

Course content differs each time it is offered.


Explanation for above repeatability selection:


9a. Grading Option:

Standard Grade

9b. Catalog Description:

Study of points, lines, angles, polygons, triangles, similarity, congruence, geometric proofs, area, volume, perimeter, the circle, right triangle trigonometry.




Course Outline Information


10. Course Objectives: (Course objectives for all credit courses must indicate that students will learn critical thinking and will be able to apply concepts at college level.  Course objectives must be related to items listed in Section 11.)

1. Name, identify, reproduce and differentiate between definitions, postulates/axioms and theorems;
2. create deductively valid proofs verifying mathematical statements concerning lines, angles, polygons and circles by using appropriate definitions, axioms or theorems, as necessary then identify, recall and demonstrate the method of indirect and direct proof;
3. cite, list and identify definitions and axioms/postulates about parallel lines; analyze properties of transversals of parallel lines and corresponding angles;
4. demonstrate the use of construction tools, particularly a compass and straight edge, to create various geometric figures (parallel lines, angle bisectors, congruent segments, equilateral triangles, perpendicular bisectors, etc);
5. verify congruency and similarity of two dimensional geometric figures by using congruence or similarity to solve for missing lengths;
6. calculate the perimeter and area of standard two dimensional figures; identify properties specific to two dimensional geometric figures;
7. apply properties of the chords, tangent lines and secants of a circle; find the area, circumference and arc length of a sector of a circle; determine relationships between angles found in a circle;
8. determine the lateral area, surface area and volume of standard three dimensional figures; and
9. apply the sine, cosine and tangent ratios of a right triangle; find the measure of an angle given the values of unknown sides using a calculator; solve right triangles and evaluate trigonometric values of special angles 30*,45*,60*.


11. Course Content Outline: (Provides a comprehensive, sequential outline of the course content, including all major subject matter and the specific body of knowledge covered.)

I. Terminology Needed for Proofs
A. Definitions
B. Axioms/Postulates
C. Theorems
II. Geometric Proofs and Logic
A. Direct Proof
B. Indirect Proof
III. Parallel Lines
A. Definition
B. Postulates
C. Transversals and Corresponding Angle Properties
IV. Construction
A. Parallel Lines
B. Angle Bisectors
C. Perpendicular Bisectors
D. Congruent Segments and Angles
E. Applications
V. Triangles
A. Sum of angles
B. Area
C. Congruence, Corresponding Parts
D. Isosceles, Equilateral
E. Similar
F. Ratio, Proportion
G. Pythagorean Theorem
VI. Polygons
A. Properties of Polygons
B. Properties of Quadrilaterals
C. Perimeter
D. Area
VII. Circles
A. Angles
B. Circumference
C. Area
D. Arcs, Sectors, Chords, Secants and Tangents
VIII. Three Dimensional Figures
A. Lateral Area
B. Surface Area
C. Volume
IX. Right Triangle Trigonometry
A. Sine, Cosine, Tangent Ratios
B. Special Angles
C. Solving Right Triangles
D. Applications


12. Typical Out-of-Class Assignments: Credit courses require two hours of independent work outside of class per unit of credit for each lecture hour, less for lab/activity classes.  List types of assignments, including library assignments.)


a. Reading Assignments: (Submit at least 2 examples)

1. Research the history of the Pythagorean Theorem and find different ways in which it has been proven.
2. Research Rene Descartes' life and his contributions to the field of geometry.


b. Writing, Problem Solving or Performance: (Submit at least 2 examples)

1. Prove the Pythagorean Theorem 2 different ways.
2. Two apartment buildings are 40 feet apart. From a window in her apartment, Sabrina can see the top of the other apartment building at an angle of elevation of 47 degrees. She can also see the base of the other building through an angle of depression of 33 degrees. How tall is the other building?


c. Other (Term projects, research papers, portfolios, etc.)


13. Required Materials:

a. All Textbooks, resources and other materials used in this course are College Level?




b. Representative college-level textbooks (for degree-applicable courses) or other print materials.

Book 1:




  Elementary Geometry for College Students


  Brooks Cole

Date of Publication:




Book 2:




  Basic Geometry for College Students



Date of Publication:




Book 3:







Date of Publication:




Book 4:







Date of Publication:




Book 5:







Date of Publication:




c. Other materials and/or supplies required of students:


Methods of Instruction


14a. Check all instructional methods used to present course content.


Laboratory and/or Activity

Distance Learning (requires supplemental form)




14b. Provide specific examples for each method of instruction checked above; include a minimum of two examples total. Reference the course objective(s) addressed by instructional method(s). Explain both what the instructor and students are expected to be doing and experiencing.

Example 1: Interactive lecture format to develop the concept of proofs. Students will name, identify, reproduce and differentiate between definitions, postulates/axioms and theorems; and create valid proofs verifying mathematical statements concerning lines, angles, polygons, and circles.

Example 2: After reading about the Pythagorean theorem, students will integrate a geometric model with an algebraic model to prove that the square of the legs of a right triangle is equal to the square of the hypotenuse.

Example 3: In class small group collaborative learning activity focusing on solving right triangles using the sine, cosine, and tangent functions.




15. Methods of Assessing Student Learning  


15a.  Methods of Evaluation:


Essay Examinations

Objective Examinations

Problem Solving Examinations

Skill Demonstrations



Classroom Discussions




Other (explain below)







15b. Based upon course objectives, give examples of how student performance will be evaluated. Provide examples for each method checked above; include a minimum of two examples total.




Example 1. Prove that if a ray is on the interior of an angle, the sum of the two smaller angles is equivalent to the largest angle.

Example 2. Using only a straight-edge and a compass, construct a rectangle of a given size.

Example 3. Complete a proof that two triangles are congruent using the method of Side-Angle-Side.

Example 4. Find the volume and lateral area of a cone with a radius of 3 and height of 17.












1. Program Information:  

In an approved program.  

Part of a new program.

Not part of an approved program.  

2. Course TOP Code:

   Program title - TOP Code:  

Mathematics, General- 170100


3. Course SAM Code:

 A  Apprenticeship

 B  Advanced Occupational

 C  Clearly Occupational

 D  Possibly Occupational

 E  Non-Occupational


4. Faculty Discipline Assignment(s):










General Education Information:  

1.  College Associate Degree GE Applicability:    

Math Competency
Communication & Analytic Thinking

2.  CSU GE Applicability (Recommended-requires CSU approval):

3.  IGETC Applicability (Recommended-requires CSU/UC approval):  

4. C-ID:  






Articulation Information:  (Required for Transferable courses only)



CSU Transferable.  

UC Transferable.

CSU/UC major requirement.  


If CSU/UC major requirement, list campus and major. (Note: Must be lower division)




List at least one community college and its comparable course.  If requesting CSU and/or UC transferability also list a CSU/UC campus and comparable lower division course.


American River College - Math 110 5 units





Planning and Resources - Please address the areas below:  

1. Evidence of Planning: connection to existing or planned degrees/certificates, place in general education; relationship to mission (basic skills, transfer, career technical education, lifelong learning); transfer university requirements; advisory/regional/national needs; or other planning considerations.

Meets the Mathematics requirement for achieving an Associate Degree. Required as a prerequisite for Math 17.
Meets the Mathematics requirement for achieving an Associate Degree. Additionally required as a prerequisite for Math 17.
Meets GE applicability for Mathematics Competency and Communication and Analytical Thinking. Course includes all four Math program SLO's (Equations and Expressions, Visual Models, Applied Problems, Communication).

2. Potential Impact on Resources: faculty, facilities, computer support/lab, library, transportation, equipment, or other needs.
All math faculty members meet the minimum qualifications to teach this course. No special training is required.
No additional resources are needed since we have the classroom space and technology already available.





1.  Maximum Class Size (recommended):              35

2.  If recommended class size is not standard, then provide rationale: