Foundations of Geometric Relationships: Honors Geometry

Honors Geometry Syllabus

Geometry Honors provides a strong foundation for students preparing for academic or technical college experiences. It uses mathematical proofs to develop two-dimensional and three-dimensional geometric concepts and properties, including transformations, Pythagorean theorem relationships, circles and constructions.

Students cultivate a solid understanding of definitions, postulates and axioms, as they construct and defend mathematical arguments. They learn to recognize patterns, understand congruence and similarity, and use Pythagorean theorem in right triangles.

Points and Lines

In this high school geometry course, students develop a foundation for understanding the fundamental concepts of geometric relationships through reasoning and proof. This online course covers the topics typically offered in a full-year honors geometry curriculum, including points and lines; parallel and perpendicular lines; circles, polygons, and three-dimensional figures; and areas and volumes of solid and plane objects.

Honors Geometry is more difficult than regular Geometry courses and requires a stronger ability to construct logical arguments. The course also teaches students how to identify two-dimensional figures and their properties, and how to transform figures in the plane by dilating, translating, reflecting, and rotating them. Students learn how to use ancient technologies (like a compass and straight edge) as well as modern tools (like graphing utilities and video tutorials) to develop skills that are used daily by carpenters, lawyers, and artists.


Students in this course explore the relationship of angles and sides of triangles to prove geometric theorems. They also analyze the relationship between angles and lines and between polygons and three-dimensional figures. This online high school geometry class builds upon student command of the elements of Euclidean and spherical geometry to advance students into higher level thinking skills.

Through this course, honors students discover how geometric relationships predict results in the real world. Using this understanding, students are better prepared to move into more challenging math courses such as Algebra II and Precalculus. This course is designed to be taught in a flexible virtual classroom environment with an experienced instructor that uses virtual meeting software to engage students through video, voice, text, and whiteboard collaboration.


From the ancient pyramids to today’s highways, geometry illuminates our world. Learners cultivate strong spatial reasoning skills as they explore points, lines, and angles; postulates, axioms, and properties of two-dimensional figures; congruence, similarity, transformations, and proof; quadrilaterals; circles; and three-dimensional solids.

Students use model-building activities to gain a deeper understanding of geometric concepts and to practice mathematical problem-solving. These lessons prepare students to synthesize their knowledge in novel real-world scenarios by asking “what if” questions and analyzing the strengths and weaknesses of their models.

This honors geometry course covers the core content typically taught in a full-year geometry course. Students develop a stronger command of geometric relationships and move toward creating logical proofs, learning to recognize and apply the Pythagorean theorem; analyze special right triangles; and discover surface area, volume, and other three-dimensional figure properties.


Students learn to prove geometric relationships using deductive reasoning and the process of logical argumentation. They discover parallel lines, polygons, and tessellations, and explore the relationship of triangles to trigonometry. They also study the properties of circles, and calculate area and volume of two-dimensional figures.

This course meets for seven weeks. Because this course counts for academic credit, students are NOT allowed to miss class. If you are going to be away for any reason, check with the teacher via email or google group to see what assignments you need to complete when you return.

Honors Geometry is designed for advanced eighth graders or high school students who have completed Algebra 1. This course combines traditional deductive reasoning with contemporary computational and discovery approaches to learning geometry.

Three-Dimensional Figures

Students learn about three-dimensional figures like prisms, pyramids, cylinders, and cones. They also study three-dimensional shapes’ cross sections and how a change in one linear dimension can affect surface area and volume.

Students analyze geometric properties, proofs, and relationships using deductive reasoning. Honors geometry students learn more advanced concepts than those in regular Geometry courses, including transformations, congruence, similarity, and right triangle trigonometry.

If your student is interested in taking a rigorous course, this online honors geometry high school class could be the right choice. However, students must be highly motivated to excel in this course as it is more challenging than Algebra 1 and regular Geometry courses. Make sure your student is prepared for honors geometry by reviewing the course syllabus and completing Algebra 1 Honors.

Leave a Reply

Your email address will not be published. Required fields are marked *