## MATH 0000B - Plane Geometry

http://catalog.sierracollege.edu/course-outlines/math-0000b/

Catalog Description Course Student Learning Outcomes CSLO #1: Logically present clear, complete, accurate, and sufficiently detailed solutions to communicate reasoning and demonstrate the method of solving problems. CSLO #2: Construct deductively valid proofs of theorems by using definitions, postulates, and previously proven theorems. CSLO #3: Using a compass and straightedge construct standard geometric figures: duplicated angle, duplicated line segment, angle bisector, perpendicular bisector, equilateral triangle, square, and the incenter, circumcenter, orthocenter, and centroid of a triangle. Effective Term Fall 2024 Course Type Credit - Degree-applicable Contact Hours 72 Outside of Class Hours 144 Total Student Learning Hours 216 Course Objectives 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*. General Education Information Approved College Associate Degree GE Applicability AA/AS - Comm & Analyt Thinking AA/AS - Mathematical Skills CSU GE Applicability (Recommended-requires CSU approval) Cal-GETC Applicability (Recommended - Requires External Approval) IGETC Applicability (Recommended-requires CSU/UC approval) Articulation Information Not Transferable Methods of Evaluation Objective Examinations 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. 2. Using only a straight-edge and a compass, construct a rectangle of a given size. 3. Complete a proof that two triangles are congruent using the method of Side-Angle-Side. 4. Find the volume and lateral area of a cone with a radius of 3 and height of 17. Repeatable No Methods of Instruction Lecture/Discussion Distance Learning Lecture: 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. (Objectives 1 & 2) Students will work in small groups carrying out a collaborative learning process focusing on solving right triangles using the sine, cosine, and tangent functions. The instructor will act as the a facilitator during this problem solving activity. (Objective 9) Distance Learning 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. (Objectives 1 & 2) Students will work in small virtual groups carrying out a collaborative learning process focusing on solving right triangles using the sine, cosine, and tangent functions. The instructor will act as the a facilitator during this problem solving activity. (Objective 9) Typical Out of Class Assignments Reading Assignments 1. Research the history of the Pythagorean Theorem and find different ways in which it has been proven and be prepared to discuss in class. 2. Research Rene Descartes' life and his contributions to the field of geometry and be prepared to discuss in class. Writing, Problem Solving or Performance 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? Other (Term projects, research papers, portfolios, etc.) Required Materials Elementary Geometry for College Students Author: Alexander/Koeberlein Publisher: Brooks Cole Publication Date: 2020 Text Edition: 7th Classic Textbook?: No OER Link: OER: Geometry Author: Elayn Martin-Gay Publisher: Pearson Publication Date: 2016 Text Edition: 1st Classic Textbook?: No OER Link: OER: Other materials and-or supplies required of students that contribute to the cost of the course.