1. Lesson 6

1.7. Explore 3

Module 2: Lesson 6

Module 2: Logic and Geometry

 

Try This 4
 

assignment

You will submit your answers from Try This 4 to your teacher for marks.

 

Discuss the method Quinn used to develop his conjecture. In your discussion, consider the following questions:

  1. How could Quinn strengthen his conjecture? (1 mark)

  2. Do you have any evidence from your observations of the Angles and Lines applet and the Parallel Lines applet that would strengthen or invalidate Quinn’s conjecture? (1 mark)

  3. Could a similar conjecture be written for alternate interior angles? What evidence do you have to support this conjecture? (2 marks)

    alternate interior angles: two interior angles formed between two lines and a transversal, on opposite sides of the transversal

     

    This illustration shows alternate exterior angles.


     

    This is a graphic showing Quinn’s conjecture.

     

Self-Check 3
  1. In each diagram, is CD parallel to EF? Explain how you know.

    1. This is a graphic of a transversal intersecting two lines. The measures of two alternate interior angles are given. One angle measures 122 degrees. The other angle measures 123 degrees.

      Answer

    2. This is a graphic of a transversal intersecting two lines. Two alternate exterior angles are shown that both measure 41 degrees.

      Answer

textbook
  1. Complete “Further Your Understanding” questions 2, 4, and 5 on page 72 of your textbook. Answer

Inductive reasoning was used to develop several conjectures about the relationships between the angles formed when a transversal intersects a pair of parallel lines. The applet Angle Relationships is a review of the different angle relationships presented in this lesson and will help you to visualize the conjectures that were developed. You will notice that pairs of angles are shown in the same colour. Make sure you only have one angle relationship selected at a time.

 

 

This is a screenshot for Angle Relationship.


notes organizer

If you haven’t done so already, now would be a good time to organize your thoughts and summarize any key ideas from this lesson in your notes organizer.