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Problem Solving in Geometry

Prerequisites: Qualifying math score and completion of at least one semester of Algebra I

Course Format: Individually Paced

Course Length: Typically 3 months

Course Code: PSG

Course Description


CTY's Problem Solving courses sharpen investigative skills, broaden mathematical understanding of concepts, and enhance reasoning skills. Designed around performance objectives that reflect national and state mathematical standards and drawing on video lectures provided by Thinkwell, these courses demonstrate how mathematical issues arise out of real-life situations. Concepts are assessed through challenging quizzes and chapter tests. 

In Problem Solving in Geometry, students apply geometric concepts to solve sets of word problems at varying levels of difficulty. This course provides an excellent foundation for students who will be advancing into Honors Geometry or Honors Algebra II.  Students will have their understanding checked with graded assessments, which include quizzes, homework, tests, and cumulative midterm and final exams.

Upon successful completion of this course, a student will be able to understand definitions and theorems as well as solve problems related to:

  • Points, Lines, Planes, and Angles
  • Angle Relationships in Polygons 
  • Triangle Congruence and Similarity
  • The Pythagorean Theorem and Its Converse
  • Properties of Quadrilaterals
  • Areas of Plane Figures
  • Volumes and Surface Areas of Solids

For a detailed list of topics, click the List of Topics tab.


Image of banner saying "Welcome to Problem Solving in Geometry."

Materials Needed

A graphing calculator is required.

List of Topics

Points, Lines, Planes, and Angles

  • Points, Lines, and Planes
  • Segments, Rays, and Distance 
  • Angles

Angles and Angle Relationships

  • Angle Relationships 
  • Properties of Parallel Lines
  • Angles of a Triangle 
  • Angles of Polygons


  • Congruent Triangles
  • Altitudes, Bisectors, and Medians
  • Triangle Similarity  
  • Similarity in Right Triangles  
  • The Pythagorean Theorem 


  • Properties of Parallelograms  
  • Special Parallelograms
  • Trapezoids and Kites

Areas of Plane Figures

  • Areas of Parallelograms, Rectangles, Rhombuses, and Kites
  • Areas of Trapezoids and Triangles
  • Areas of Regular Polygons
  • Circumference and Area of Circles

Areas and Volumes of Solids

  • Prisms and Pyramids
  • Cylinders and Cones
  • Spheres


Open Help Room

Each week, all students are invited to a Problem Solving Open Help Room run by a rotating staff of instructors. Students are encouraged to come with questions or just to meet other online students. Topics reviewed vary each week. 

The Problem Solving Open Help Room meets each Tuesday from 7 – 8 p.m. EST. 


Sample Video Lecture

Sample Video

Problem Solving in Geometry video

Technical Requirements

Technical Requirements

This course requires a properly maintained computer with high-speed internet access and an up-to-date web browser (such as Chrome or Firefox). The student must be able to communicate with the instructor via email. Visit the Technical Requirements and Support page for more details.

This course uses an online virtual classroom for discussions with the instructor. The classroom works on standard computers with the Adobe Connect Add-in or Adobe Flash plugin, and also tablets or handhelds that support the Adobe Connect Mobile appStudents who are unable to attend live sessions will need a computer with the Adobe Connect Add-in or Adobe Flash plugin installed to watch recorded meetings. The Adobe Connect Add-in, Adobe Flash plugin, and Adobe Connect Mobile app are available for free download. Students who do not have the Flash plug-in installed or enabled on their browsers will be prompted to download and install the Adobe Connect add-in when accessing the virtual classroom.