Beyond IQ

Proving the Point:
A Perigon of Geometry

Register for Proving the Point: A Perigon of Geometry here! 

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Instructor: Lisa Fontaine-Rainen
3-8 students
Suggested Age Range: 11+
Meets: Tues 3-4pm, Thu 4:30-5:30pm



What happens when you make that point?  What if you draw this line in the sand?  Geometry may sound a lot like arguing, but the deductive logic behind it makes those arguments, well, pointless.

Proving the Point: A Perigon of Geometry is an advanced, fast-paced high-school level geometry course that encourages deep understanding of geometric concepts, with an emphasis on Euclidean geometry, and deductive reasoning to construct proofs.  We will be working on completing a full Geometry curriculum in 16 weeks.

The course is designed to meet the needs of gifted and twice exceptional students ready to tackle high school geometry.  In response to the needs of these students, the course is designed to be flexible and responsive – thinking, learning, and engagement take precedence over all else.  With this in mind, the syllabus may change based on the needs of the students.

This course will weave Geometry: Seeing, Doing, Understanding by Harold Jacobs with Art of Problem Solving’s Introduction to Geometry.  Students are encouraged to have access to both texts – please contact the instructor directly if this is a financial hardship.

Students will need to do homework outside of class to ensure we can keep up the pace.  This will include in-depth problems, simple exercises, proofs, quizzes and tests, and projects.  Work will be modified based on the learning needs of each student, and opportunities for further exploration will usually be provided.  Grades are optional – learning is constant.


Week 1: Introduction to Geometry

Week 2: Introduction to Deductive Reasoning

Week 3: Lines and Angles – an introduction to construction

Week 4: Congruence – Triangles and Constructions

Week 5: Inequalities in Geometry

Week 6: Parallel Lines and Proofs

Week 7: Quadrilaterals

Week 8: Transformations

Week 9: Area

Week 10: Similarity

Week 11: The Right Triangle – an introduction to Trigonometry

Week 12: Circles

Week 13: Concurrence Theorems

Week 14: Regular Polygons

Week 15: Geometric Solids

Week 16: Non-Euclidean Geometries

Register for Proving the Point: A Perigon of Geometry here!  

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