Modern Geometries

Course Code:

Credit Hours:

Effective beginning:



Course Description:
This course is designed for in-service middle and high school teachers and for students who are majoring in secondary mathematics education. It 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 geometries. There is emphasis on making conjectures and constructing proofs concerning geometrical relationships.


Course Details


MAC 2312



As assigned


Required textbooks/ course materials:

College Geometry: A Problem-Solving Approach with Applications, Musser, Trimpe, Maurer, 2nd ed., 2008.  Pearson Education, ISBN: 9780321656773  


Assignment/course outline:

See your Instructor First Day Handout.


Discipline-level learning outcomes:

E – 1 Demonstrate understanding of instructional design and lesson planning by applying concepts from human development and learning theories.

E – 2 Demonstrate ability to maintain a student-centered learning environment that is safe, organized, equitable, flexible, inclusive and collaborative.

E – 3 Demonstrate effective instructional delivery and facilitation by utilizing deep and comprehensive knowledge of core content.

E – 4 Demonstrate understanding of assessment by analyzing and applying data from multiple assessments to diagnose learning needs and inform instruction.

E – 5 Demonstrate continuous improvement by designing purposeful goals to strengthen instructional effectiveness and impact student learning.

E – 6  Demonstrates professional responsibility and ethical conduct and fulfills expected obligations to students, the public, and the education profession.

MTG 3212 is not a General Education core course.


Course-level learning outcomes:

Course-level student learning outcomesDiscipline-level learning outcomesAssessment methods

Formulate conjectures, proofs, and counterexamples using axiomatic geometry.

Construct geometric figures using compass and straight edge, and interactive geometry software.

Solve problems involving the relationships among points, lines and planes.

Solve triangle problems using trigonometry and the Pythagorean Theorem.

Solve problems involving circles, polygons, and irregular planar figures.

Solve problems involving regular and irregular solids.

Solve problems using coordinate geometry.

Construct proofs using congruence theorems, similarity, and properties of geometric figures.

Solve problems using dimensional analysis.

Identify properties of non-Euclidean geometries.

Solve basic problems involving non-Euclidean geometries. 


Homework, Report/Presentation, Unit Test, Final Exam


Means of accomplishing learning outcomes:

Teacher facilitated: The instructor will be leading class discussions on the material during class periods.

Student-centered: The students will practice solving problems and make several presentations during class periods.

Office Hours: The instructor will be available during office hours for individual assistance.


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