# 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

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
• Areas of Plane Figures
• Volumes and Surface Areas of Solids

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

## 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

#### Triangles

• 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

## Problem Solving Help Room

Help Room

Each week, all students are invited to a Problem Solving 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 Help Room meets each Tuesday from 7 – 8 p.m. ET.

Sample 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.