Inductive Reasoning

The process of observing data, recognizing patterns and making generalizations about those patterns.

Conjectures A statement you believe is true but is unproven. When you use inductive reasoning to make a generalization, the generalization is called a conjecture We just made a conjecture about the pattern in the previous slide.

Pattern WAR! Work together as a group and construct your own number or picture pattern. Switch your pattern with another group. Now, work as a group to make a conjecture about the rule and find the next term.

Quiz-Quiz-Trade 1.Answer your question on the back of your notecard. (May already be done for you) 2.Stand up-Hand up-Pair up 3.Quiz your partner providing hints when necessary. Then switch roles. 4.Trade your card, then go back to 2.

Deductive Reasoning The process of showing that certain statements follow logically from agreed- upon assumptions and proven facts. You are trying to prove to yourself or someone else that your conclusion is valid

Draw a Venn Diagram that shows the relationship between quadrilaterals, squares, rectangles, rhombuses, trapezoids, isosceles trapezoids, parallelograms and kites. Then write 5 conditional statements shown in your Venn Diagrams.

1 -Make a conjecture (using what kind of reasoning?) 2 - Explain why it’s true (now what kind of reasoning?)

If an obtuse angle is bisected, then the two newly formed congruent angles are

Now let’s prove it…

Inductive vs. Deductive Reasoning Inductive Reasoning –Looking at specific examples to make a generalization. –Used to make discoveries/conjectures. Deductive Reasoning –Using generalizations to make a specific conclusion. –Used to prove conjectures.

An example of a logical deduction that is true. All angles between 90 and 180 degrees are obtuse. Angle Q is 120 degrees. Conclusion: Angle Q is obtuse.

Exit Ticket Every time you go to your locker before heading to the cafeteria, you have to wait on a long line. When you go to the cafeteria right from class, you get your lunch right away. If you skip the locker trip on your way to the cafeteria because you are really hungry and do not want to wait on a long line, what type of reasoning are you using?

HW: Read p. 96 – 99, p. 99, 2, 3-9 (odd), 11-15, 17, Read p. 114, Do p. 117, 1, 3, 9, 26, 28, 30, 31