1. Entry Task Complete each sentence. 1. ? points are points that lie on the same line. 2. ? points are points that lie in the same plane. 3. The sum of the measures of two ? angles is 90°. Collinear Coplanar complementary

2. Do NOW – DISCUSS WITH YOUR TABLE

3. 2.1 Using Patterns and Inductive Reasoning Learning Target I can use inductive reasoning to make a conjecture.

4. inductive reasoning Conjecture Counterexample Vocabulary pg 82

5. Find the next item in the pattern. Example 1: Identifying a Pattern January, March, May,... The next month is July. Alternating months of the year make up the pattern.

6. Find the next item in the pattern. Example 2: Identifying a Pattern 7, 14, 21, 28, … The next multiple is 35. Multiples of 7 make up the pattern.

7. Find the next item in the pattern. Example 3: Identifying a Pattern In this pattern, the figure rotates 90° counter- clockwise each time. The next figure is.

8. When several examples form a pattern and you assume the pattern will continue, you are applying inductive reasoning. Inductive reasoning is the process of reasoning that a rule or statement is true because specific cases are true. You may use inductive reasoning to draw a conclusion from a pattern. A statement you believe to be true based on inductive reasoning is called a conjecture.

9. Complete the conjecture. Example 4: Making a Conjecture The sum of two positive numbers is ?. The sum of two positive numbers is positive. List some examples and look for a pattern. 1 + 1 = 23.14 + 0.01 = 3.15 3,900 + 1,000,017 = 1,003,917

10. Check It Out! Example 5 The product of two odd numbers is ?. Complete the conjecture. The product of two odd numbers is odd. List some examples and look for a pattern. 1  1 = 1 3  3 = 9 5  7 = 35

11. Check It Out! Example 6 Make a conjecture about the lengths of male and female whales based on the data. In 5 of the 6 pairs of numbers above the female is longer. Female whales are longer than male whales. Average Whale Lengths Length of Female (ft) 495150485147 Length of Male (ft) 4745444648

12. To show that a conjecture is false, you have to find only one example in which the conjecture is not true. This case is called a counterexample. To show that a conjecture is always true, you must prove it. A counterexample can be a drawing, a statement, or a number. Inductive Reasoning 1. Look for a pattern. 2. Make a conjecture. 3. Prove the conjecture or find a counterexample.

13. Determine if each conjecture is true. If false, give a counterexample. 1. The quotient of two negative numbers is a positive number. 2. Every prime number is odd. 3. Two supplementary angles are not congruent. 4. The square of an odd integer is odd. false; 2 true false; 90° and 90° true

14. HW #11 Pg 85-88 #6-30 evens #34-42 evens