MTG 3212 - Modern Geometries

College of Education

Credit(s): 4
Contact Hours: 62
Effective Term Spring 2026 (660)

Requisites

Prerequisite MAC 2311 with a minimum grade of C

Course Description

This course presents the axioms, basic concepts, proofs and constructions of Euclidean geometry involving line segments, angles, triangles, polygons, circles, parallel lines and similarity. Constructions are made using both compass and straightedge and interactive geometry software. The course also presents basic concepts of non-Euclidean geometries including hyperbolic and spherical. Students will use technology to make conjectures and discoveries concerning geometrical relationships and construct geometric proofs.

Learning Outcomes and Objectives

  1. The student will solve problems using the axioms and basic concepts of Euclidean plane geometry by:
    1. explaining Euclid’s fundamental axioms for plane geometry.
    2. identifying the underlying Euclidean concepts of a set of points in a two-dimensional plane, length, lines, circles, angular measure and congruence.
    3. classifying and applying transformations (translations, rotations, dilations, or reflections).
    4. analyzing properties of images and preimages.
    5. applying the congruence theorems for triangles (SSS, SAS, ASA, AAS, and HL).
    6. examining geometric constructions using both compass, straight edge and geometric software.
  2. The student will explain the formulation of conjectures involving line segments, angles, triangles, polygons, and circles by:
    1. identifying and applying properties of geometric figures.
    2. using analytic reasoning to formulate conjectures.
    3. using interactive geometry software to formulate conjectures.
    4. proving and applying theorems pertaining to geometric figures.
  3. The student will summarize the properties of regular and semi-regular polyhedra by:
    1. identifying characteristics of three-dimensional figures (e.g., faces, edges, vertices).
    2. identifying the net of a three-dimensional figure.
    3. identifying the two-dimensional view of a three-dimensional object.
    4. analyzing regular and semi-regular polyhedra.
    5. investigating the Euler characteristic of a polyhedron.
  4. The student will solve problems using the basic concepts of spherical and hyperbolic geometry by:
    1. using the fundamental axioms for spherical and hyperbolic geometry.
    2. analyzing the difference between the parallel postulate of spherical and hyperbolic geometry and that of Euclidean geometry.
    3. verifying that the sum of the measures of the angles in a spherical triangle exceeds 180 degrees.
    4. verifying that the sum of the measures of the angles in a hyperbolic triangle is less than 180 degrees.
    5. computing spherical areas.
    6. investigating the Pythagorean theorem for spherical and hyperbolic geometry.
    7. determining the law of sines and cosines for spherical and hyperbolic geometry.

Criteria Performance Standard

Upon successful completion of the course, the student will, with a minimum of 75% accuracy, demonstrate mastery of each of the above stated objectives through classroom measures developed by individual course instructors.

History of Changes

C&I 3/12/02, BOT 4/16/02, Effective yrtr 20021. 2005 3 Year Review done 2006, effective 20061(0370). C&I 12/4/07, BOT 1/15/08, Effective 20072(0390). Flex access 20081(0400). C&I 4/13/2010, BOT 5/18/2010, Effective 20093(0425). C&I Approval: 01/20/2012, BOT Approval: 02/21/2012, Effective Term: Fall 2012 (460).
C&I Approval: , BOT Approval: , Effective Term: Spring 2026 (660)

Related Programs

  1. Secondary Education Mathematics (6-12) (MTSED-BS) (645) (Active)