1. Lesson 9

1.5. Explore 4

Module 2: Lesson 9

Module 2: Logic and Geometry

 

In the preceding Share activity, you and your partner were asked to make a conjecture about the relationship between an exterior angle and its two non-adjacent interior angles. Zahia and her partner made the following conjecture.

 

This is a photo of a conjecture written on a screen stating that an exterior angle of a triangle is equal to the sum of the measures of the two non-adjacent interior angles.

iStockphoto/Thinkstock

 

Use the Exterior Angles of Triangles applet to see if Zahia’s conjecture holds true for other triangles. Drag the orange dots on any vertex to reshape the triangle.

 

 

This is a screenshot for Exterior Angles of Triangles.


textbook

The Exterior Angles of Triangles applet illustrates the relationship between the exterior and interior angles of a triangle. Read “Example 2: Using reasoning to determine the relationship between the exterior and interior angles of a triangle” on page 88 of your textbook to see a proof of this relationship. As you read through Joanna’s proof, consider how she uses angle properties you have learned in previous lessons to prove the relationship between an exterior angle of a triangle and the two non-adjacent interior angles.

Self-Check 2

 


textbook
  1. Complete “Check Your Understanding” question 3 on page 90 of your textbook. Answer

  2. Complete “Practising” questions 5, 6, 8, and 9 on page 91 of your textbook. Answer