Lesson 9
1. Lesson 9
1.8. Explore 7
Module 2: Logic and Geometry
The properties of angles can be used to solve problems. As you have seen, sometimes the properties can be combined in different ways to solve the same problem. As long as the reasoning used is correct and you have applied the angle properties correctly, many strategies will give a correct solution to the problem. You will find that some strategies may be more efficient than others; e.g., some strategies may require fewer steps. It is important to understand that the key to solving problems involving angle properties is to use strategies that apply correct methods and reasoning regardless of how many steps are required.
Read “Example 3: Using reasoning to solve problems” on pages 88 and 89 of your textbook to see personal strategies Tyler and Dominique used for solving the same problem. As you read over their solutions, consider the following questions.
- Which of the two strategies shown in the textbook do you prefer?
- Do you see a strategy you like better than the strategies used by Tyler and Dominique?
- Think about the strategy you prefer. Are there angle relationships you find easier to identify? Do you prefer working with angles in triangles? Do you prefer working with angles related to parallel lines?
Remember that your strategy may differ from others, but as long as you apply the angle properties correctly and use correct reasoning, you can still find the same solution to a problem.
Self-Check 3
Complete “Practising” questions 11, 12, 13, and 15 on page 92 of your textbook. Answer
If you haven’t done so already, now is a good time to update your notes organizer. A good starting point is to reflect on how drawing a line that is parallel to one side of any triangle can help you prove that the sum of the angles in a triangle is 180°. You may find the ideas presented in the “In Summary” section on page 90 of your textbook useful.