MATH 086 - Essentials of Geometry

5 Credits

A geometry course that examines important properties of 2-D and 3-D shapes, including area, volume, congruence, similarity, constructions, transformations, and trigonometry. The course emphasizes using inductive and deductive reasoning to make claims and establish their validity.

Pre-requisite(s) MATH 081 min 2.0
Placement Eligibility Math 091 or higher
Fees

Quarters Typically Offered

Winter Day

Designed to Serve Students who need to earn credit for a high school geometry course, or who would like a review of fundamental concepts of 2-D and 3-D geometry.
Active Date 2013-06-14

Grading System Decimal Grade
Class Limit 25
Shared Learning Environment Yes
Contact Hours: Lecture 55 Lab 0 Worksite 0 Clinical 0 Other 0
Total Contact Hours 55
Degree Distributions:
Course Outline
Topics may vary slightly, but will include the following: * Right-triangle trigonometry - define and compute both distances and angles in realistic situations * Lines and angles - notation, definitions, line and angle relationships, the Pythagorean Theorem; begin practicing reasoning inductively and deductively * Geometric constructions - manually copy, bisect, create parallel and perpendicular lines, build shapes, explore properties of shapes using technology, continue hypothesizing and justifying * Congruence and similarity - define, verify, and solve problems using congruence or similarity of triangles * Geometric proof - justify properties of lines, angles, and shapes arising earlier in the course * Coordinate geometry - revisit concepts of position, distance, angles (slope), midpoints, collinearity, parallelism, and perpendicularity using coordinates and basic algebra * Transformations - perform translations, reflections, and some rotations, then describe the effects of translations and reflections on coordinates of points. * Analyze 3-D shapes - classify and represent basic 3-D shapes; define, justify formulas for, and calculate surface area and volume; and empirically verify pi.

Student Learning Outcomes
State, justify, and use theorems about angles - especially about angles formed when parallel lines are intersected by a transversal.

State, justify, and use the Pythagorean Theorem to solve problems.

Define triangle congruence and similarity and use them to determine if triangles are congruent or similar, as well as to solve real-world problems.

Perform geometric constructions by hand and using geometry software.

Describe and compute locations, distances, and directions using coordinates and algebra.

Define and apply basic isometries to 2-D shapes.

Define and solve problems involving the basic trigonometric ratios of sine, cosine, tangent, and their inverses.

Define, compare, and represent prisms, pyramids, cylinders, cones, and spheres.

Define, justify, and compute with formulas for surface area and volume.

Inductively generate conjectures and either support them deductively or refute them with counterexamples.