» Please sit by your number from the seating chart on the clipboard. » Please fill in the vocabulary sheet on your desk: ˃Conditional statement ˃Hypothesis.

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Presentation transcript:

» Please sit by your number from the seating chart on the clipboard. » Please fill in the vocabulary sheet on your desk: ˃Conditional statement ˃Hypothesis ˃Conclusion ˃Converse ˃Inverse ˃Contrapositive

2-1 & 2-4

» Inductive Reasoning: ˃Reasoning based on patterns you observe ˃You have to LOOK for a pattern!!!

» Conjecture: ˃Conclusion reached by inductive reasoning ˃Make sure you have ENOUGH data What conjecture can we make about the number of regions 20 diameters will make? What conjecture can we make about the 21 st term of R, W, B, R, W, B…

» Counterexample: ˃Example used to prove a conjecture is FALSE If the name of a month starts with the letter J, it is a summer month. You can connect any 3 points to form a triangle. When you multiply a number by 2, the product is greater than the original number.

» Deductive Reasoning ˃Processing of reasoning logically from GIVEN statements/facts to make a CONCLUSION If we are GIVEN a TRUE statement, then we can make a VALID or TRUE conclusion.

» Law of Syllogism SymbolExample If p → q is true and q → r is true, then p → r is true. If it is July, then you are on summer vacation. If you are on summer vacation, then you work at a smoothie shop. Conclusion: If it is July, then you work at a smoothie shop.

If both statements have the same conclusion, you can NOT use the Law of Syllogism. If you do gymnastics, then you are flexible. If you do ballet, then you are flexible.

» Exit Slip!! » If you live in Accra, then you live in Ghana. » If you live in Ghana, then you live in Africa. » Aissa lives in Accra. 1. Use the Law of Syllogism to make your 1 st conclusion. 2. Use the Law of Detachment to make you 2 nd conclusion.

» Law of Detachment LawSymbol If the HYPOTHESIS of a true conditional is true, then the CONCLUSION is true. If p → q is true and p is true, then q is true. Given: If a student gets an A on a final exam, then the student will pass the course. Felicia got an A on her history final exam. Conclusion:

Example 1. Given:If a ray divides an angle into 2 congruent angles, then the ray is an angle bisector. divides so that Conclusion: Example 2. Given:If 2 angles are adjacent, then they share a common vertex. and share a common vertex Conclusion: