# Geometry

## Introduction

This page contains resources that may be of interest to students studying Geometry. The number of resources on this page will grow as additional items are developed. If you have any questions or special requests, please contact Earl at mathguy.us@gmail.com.

## Formal (Honors) Geometry Chapter Reviews

The value of reviewing these problems and solutions is twofold. The more obvious benefit relates to problems that a student has difficulty solving themselves; a solution is provided. Less obvious is the set of techniques used in the solutions; some of the techniques used on the sample problems may not be taught in the classroom. We concentrate on efficient solutions and shortcuts; so a review of the solved problems may present new techniques that enable a student to be more efficient in their approach to solving problems.

- Algebra Review Problems and Solutions - Factoring, operations with binomials, simultaneous equations.
- Chapter 1 Review Problems and Solutions - Basic concepts: segments, midpoints, angles, bisectors, distance.
- Chapter 2 Review Problems and Solutions - Conditional statements, introduction to proofs.
- Chapter 4 Review Problems and Solutions - Triangle congruences, angle theorems, isosceles triangles.
- Chapter 5 Review Problems and Solutions - Triangle inequalities, altitudes, medians, centroid of a triangle.
- Chapter 6 Review Problems and Solutions - Quadrilaterals.
- Chapter 7 Review Problems and Solutions - Similar triangles, dilation.
- Chapter 8 Review Worksheet 1 Problems and Solutions - Pythagorean Theorem, special triangles, introduction to Trigonometry.
- Chapter 9 Review Problems and Solutions - Circles.
- Chapter 10 Review Problems and Solutions - Area and Perimeter.
- Chapter 11 Review Problems and Solutions - Solids.

## Regular Geometry Chapter Reviews - Prior Years

- 2011-12 "Area of Regular Polygons" Sample Test - Questions and Solutions – 2012 practice test and step-by-step solutions for the Area of Regular Polygons.
- 2011-12 Unit 8 Sample Test - Problems and Solutions – 2013 Practice test and step-by-step solutions for Solving Triangles and Surface Area of Solids.
- 2011-12 Semester 2 Practice Final Questions and Solutions – 2012 Semester 2 sample final and step-by-step solutions.
- 2013-14 Semester 2 Practice Final (Instructional Materials) – June 2014 Semester 2 practice final and step-by-step solutions.

## Handbooks

Students of Geometry may find the following Handbooks useful as references.

- Pre‐Algebra Handbook version 2.5 – Covers math subjects for grades 6, 7 and 8.
- Algebra and PreCalculus Handbook version 3.5 – Covers two years of Algebra and one year of Pre-Calculus.
- Geometry Handbook version 4.2 – Covers High School Geometry, Honors Geometry, and Formal Geometry.
- Trigonometry Handbook version 2.4 – Covers High School Trigonometry.

For more information on the handbooks, including download instructions, go to the Math Handbook page.

## PC Apps

There is no specific Geometry App, but when the student begins to study basic Trigonometry, the Trigonometry App may be of interest.

- Trigonometry App version 0.7g – Covers topics in Trigonometry.

For more information on the PC Apps, including download instructions, go to the PC Apps page.

## Euler Line Challenge

Here's a very cool problem that has been around for a very long time. Prove that the Centroid (intersection of medians), Orthocenter (intersection of altitudes) and Circumcenter (intersection of perpendicular bisectors) of any triangle lie on the same line. (Note: this line is called the Euler Line.)

Try to prove this yourself. One solution is provided below.

- Euler Line Challenge Solution - solution using Coordinate Geometry.