# Indirect Euclidean Proofs Worksheets

What Are Indirect Euclidean Proofs? There are times where you do have enough evidence to prove something to be true. With the foundational knowledge of a system you may not have enough information, but you can arrive at a conclusion by exploring the entire system. Under these circumstances we can support our claim or assertion that something is true by proving that alternative conclusions are completely false. For example, let’s say you wanted to prove the course of the current weather, but you did not have the ability to see the sky. There are many different instruments that could provide you measures remotely to determine this such as precipitation, air pressure, wind changes and so on. In most cases, when writing proofs, indirect statements are used to prove something is not true. Euclidean geometry is the most primitive form of mathematical proofs. It is often used to validate calculations or assertions. It is based on five of Euclid’s theorems. When we are applying this indirect form of proof writing to this, we are attempting to refer to those postulates and stating that they do not apply for one reason or another. The worksheets that you can see below will help walk you through using this form of proof writing.

• ### Basic Lesson

Guides students through the basic use of Indirect Euclidean Proofs.

• ### Intermediate Lesson

Demonstrates how to work with multi-part Indirect Euclidean Proofs. Example: If two parallel lines are cut by a transversal, the alternate interior angles are congruent.

• ### Independent Practice 1

A really great activity for allowing students to understand the concepts of the Indirect Euclidean Proofs.

• ### Independent Practice 2

Students use Indirect Euclidean Proofs in 20 assorted problems. The answers can be found below.

• ### Homework Worksheet

Students are provided with 12 problems to achieve the concepts of Indirect Euclidean Proofs.

• ### Skill Quiz

This tests the students ability to understand Indirect Euclidean Proofs.

• ### Homework and Quiz Answer Key

Answers for the homework and quiz.

• ### Lesson and Practice Answer Key

Answers for both lessons and both practice sheets.

• ### Basic Lesson

Guides students through solving Indirect Euclidean Proofs.

• ### Intermediate Lesson

Demonstrates the concept of advanced skill while solving Indirect Euclidean Proofs. Answer the following questions based on the above figure.

• ### Independent Practice 1

A really great activity for allowing students to understand the concepts of the Indirect Euclidean Proofs.

• ### Independent Practice 2

Students use Indirect Euclidean Proofs in 20 assorted problems. The answers can be found below.

• ### Homework Worksheet

Students are provided with 12 problems to achieve the concepts of Indirect Euclidean Proofs.

• ### Skill Quiz

This tests the students ability to understand Indirect Euclidean Proofs.

• ### Answer Keys

Answers for all lessons and independent practice.

#### Author Unknown

"An engineer thinks that his equations are an approximation to reality. A physicist thinks reality is an approximation to his equations. A mathematician doesn't care."