1. Lesson 7

1.4. Explore 3

Module 2: Lesson 7

Module 2: Logic and Geometry

 

Try This 1
 

assignment

You will submit your answer from Try This 1 to your teacher for grading.

 

Go to the Lesson 7 Assignment that you saved to your course folder. Complete Try This 1. Remember to save your updated Lesson 7 Assignment to your course folder.

 

Share 1
 

Present your proof from Try This 1 to another student or appropriate partner. Can you find any errors in each other’s proofs? If so, this makes the proofs invalid. Carefully identify those errors in reasoning. Can these errors be corrected to make the proofs valid? If so, make any necessary corrections in the proof.

The cellphone tower example shows that there may be multiple approaches for creating a valid proof. Each person used the angle properties in a certain way to prove that the braces on the cellphone tower were, in fact, parallel. It also shows the importance of having proofs that are free of errors. If any error occurs, the proof is invalid. Any errors in reasoning could have severe consequences. The cellphone tower braces would not be parallel and would not be constructed properly.

 

Creating a proof is much like solving a crime. A person needs to survey the crime scene, gather the facts, and then show step by step who committed the crime. It is important to include as much supporting evidence as possible so the judge and jury will be convinced that the crime has been solved. If there is an error in reasoning, an innocent person may be convicted or a guilty person may go free.

 

Consider the following example.

 

Amos was asked to prove if line MN was parallel to line OP.

 

 

This illustration is of two lines intersected by a transversal.

 

He completed the following proof:

 

Statement

Justification

∠MXY = 84°

Given

∠MXY = ∠SXN

Vertically opposite angles are equal

∠SXN = 84°

Transitive property

∠NXY = 180° − ∠SXN

 

∠NXY = 180° − 84°

 

∠NXY = 106°

Straight angles = 180°

Corresponding angles are equal: ∠NXY = ∠PYT

 

Amos has proven that MN is parallel to OP.

 

Before he hands in his assignment, he asks Miranda to check it over. She tells him that his proof is invalid. Where did he make a mistake? Can you find it?

 

Amos made a subtraction error in step 4: 108° − 84° = 96°

 

This means that ∠NXY ≠ ∠PYT, so MN is not parallel to OP.

 

Remember to always check over your proof for any errors.

 

Self-Check 3

 


textbook
  1. Complete “Practising” questions 7, 8, 16, and 19 on pages 79 to 82 of your textbook. Answer

If you feel you need more practice with proofs, complete the following questions.

  1. “Check Your Understanding” question 1 on page 78 of your textbook Answer

  2. “Practising” questions 3 and 10 on pages 79 and 80 of your textbook Answer

notes organizer

Read the “Mid-Chapter Review” on page 84 of your textbook. You may want to add some of the points presented on this page to your notes organizer.