# MATH 1312 - Introduction to Mathematical Reasoning

***This is a course guideline. Students should contact instructor for the updated information on current course syllabus, textbooks, and course content***

**Prerequisites**: A satisfactory score on a placement examination. **Note: May not apply toward a degree from the College of Natural Sciences and Mathematics.*

**Textbook**: Elementary Geometry for College Students, Daniel C. Alexander and Geralyn M. Koeberlein, 6th edition, Houghton Mifflin Company, 2015, 2011: (Summer 2019: 6 TH ED. **ISBN**: 9781285195698) (Fall 2019 & thereafter: 7 TH ED. **ISBN**: 9781337614085)

**Course Description**: Credit 3 hours (3-0). Principles of logic and proof, set theory, formal and informal geometry.

**Supplies**: A small ruler and compass will be needed for some sections and a calculator will be needed for most sections.

**Note: The information contained in this class outline is an abbreviated description of the course.** Additional important information is contained in the **Departmental Course Policies** statement and at your instructor’s personal webpage. **You are responsible for knowing all of this information*.

**Syllabus:**

Chapter 1 —Foundations of Geometry

1.1 Inductive and Deductive Reasoning

1.2 Points, Lines, and Planes

1.3 Segments, Rays, and Angles

1.4 Introduction to Deductive Proofs

1.5 Formalizing Geometric Proofs

1.6 Relationships: Parallel and Perpendicular Lines

1.7 Formal Proofs of Theorems

Chapter 2 — Triangles

2.1 Classifying Triangles

2.2 Congruent Triangles

2.3 Proofs Involving Congruence

2.4 Isosceles Triangles, Medians, Altitudes, and Concurrent Lines

2.5 Proving Right Triangles Congruent

2.6 Constructions Involving Triangles

Chapter 3 —Parallel Lines and Polygons

3.1 Indirect Proof and the Parallel Postulate

3.2 Transversals and Angles

3.3 Polygons and Angles

3.5 Define and Use Triangle Inequality Theorems

Chapter 4 — Quadrilaterals

4.1 Parallelograms

4.2 Rhombus and Kite

4.3 Rectangles and Squares

4.4 Trapezoids

Chapter 5 — Similar Polygons and the Pythagorean Theorem

5.1 Ratio and Proportion

5.2 Similar Polygons

5.3 Properties of Right Triangles

5.4 Pythagorean Theorem

5.5 Inequalities Involving Triangles

5.6 Segments Divided Proportionally in Triangles

Chapter 6 — Circles

6.1 Circles and Related Segments and Angles

6.2 More Angle measures in a Circle

6.3 Line and Segment Relationships in the Circle

6.6 Concurrence of Lines

Chapter 7 — Area of Polygons and Circles

7.1 Area and Initial Postulates

7.2 Perimeter and Area of Polygons

7.3 Regular Polygons and Area

Chapter 8 — Solid Geometry

8.1 Planes and Polyhedrons

8.2 Prisms

8.3 Pyramids

8.4 Cylinders and Cones and Spheres

**Homework:**

Section | Exercises |
---|---|

1.1 | #3, 4, 13, 15, 17, 25, 27, 29, 33, 34, 39, 41, 43, 55 |

1.2 | #3-7, 9, 11-15, 19, 21, 24, 35-39, 41-43, 46 |

1.3 | #1-6, 11, 14-17, 25, 29, 31 |

1.4 | #1, 3, 5-8, 10-13, 15, 17, 19, 21, 25, 31, 34 |

1.5 | #7-10, 11, 14, 15, 17, 25, 29 |

1.6 | #1, 3, 5, 8, 9, 11 |

1.7 | #9-15, 17, 21 |

2.1 | #1-4, 9, 15, 19 |

2.2 | #1, 3, 5, 9, 13, 17 |

2.3 | #1, 3, 5, 7, 9, 11, 17, 23, 25 |

2.4 | #1, 3, 5, 7, 9, 11, 13, 19, 23, 31, 33, 38-40 |

2.5 | #3-25 odd, 31, 35 |

2.6 | #5, 7, 13, 23, 29 |

3.1 | #1, 8-19, 21, 25, 27, 31 |

3.2 | #1, 3, 5, 11, 17, 19, 27 |

3.3 | #5, 7, 9, 11, 15, 17, 19, 21, 23, 29, 33 |

3.5 | #1, 2, 3, 11, 15, 17, 19, 21, 25 |

4.1 | #3, 5, 7, 9, 17, 21, 25 |

4.2 | #1, 7, 9, 11, 19, 25, 29 |

4.3 | #1, 3, 5, 9, 13, 17, 27 |

4.4 | #11, 13, 15, 25 |

5.1 | #5, 7, 9 ,15 , 17, 21, 29 |

5.2 | #1, 9, 13, 15, 17, 21, 29 |

5.3 | #5, 7, 9, 11, 17 |

5.4 | #7, 9, 13, 15, 17, 21, 27 |

5.5 | #1, 3, 5, 7, 9, 13, 20 |

5.6 | #5,7, 9, 13, 17 |

6.1 | #1, 3, 5, 9, 13, 19 |

6.2 | #1,3, 7, 15 |

6.3 | #1,3, 7, 15, 19 |

6.6 | #1-7, 11, 17, 27 |

7.1 | #1, 9, 11, 13, 17, 19, 27 |

7.2 | #1, 5, 9, 13, 15, 33 |

7.3 | #9, 13, 15, 17, 19, 25 |

8.1 | #1, 5, 7, 9, 15 |

8.2 | #5, 7, 9, 11, 21 |

8.3 | #3, 5, 7, 13, 15, 21 |

8.4 | #7, 23, 29 |

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