1. Informal Approach Section 1.5

2. So far our “informal way”: Led to interesting and practical results Made simple constructions … but do not know how or why they work Guessed conclusions based on appearances … not always certain they are true This is unsatisfactory … we have no basis to know if conclusions are correct!!!

3. Like Egyptians 4,000 years ago: Accumulation of rules and results based on trial and error Satisfied with ideas that appeared to be useful … without questioning why they might (or might not) be true

4. Ancient Egyptians: Formula for area of fields Area = ¼(a + c)(b + d) Based on: area of quadrilateral = product of average lengths of opposite sides b ac d L L WW Only works for a rectangle (overstates all other quads)

5. Leads us to: Critical thinking Careful analysis Provocative problems (bisect, trisect)

6. Leads to questions: How to prove something is impossible? How to tell the difference between something that is exactly right and almost right? How to prove something?

7. Types of Reasoning: Inductive Reasoning: Drawing conclusions from a limited set of observations. Deductive Reasoning: Use of logic to draw conclusions from statements already accepted as true.

8. Homework: Read pages 6 and 30 – 31 Do page 31 #1 – 15 (need compass and protractor)