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### 2.2 p1 notes

1. 1. 2.2 Conditional Statements September 01, 2011 Bellwork 1. What is the definition of conjecture?  A guess based on observation 2. Write the next number in the sequence 1, 5, 9, 13,...         17 3. A _______ disproves a conjecture.     counterexample 4. (­4)(7)+2 ­ 1=?      ­27 5. Are you lost yet in chapter 2?HW pg. 82 #3­5, 7­15, 31 & 32 1
2. 2. 2.2 Conditional Statements September 01, 2011 2.2 Analyze Conditional Statements Conditional Statement: logical statement that has 2 parts- hypothesis & conclusion written in if-then form Ex. If it is raining, then there are clouds in the sky. Rewrite the conditional statement in if-then form. All birds have feathers. If an animal is a bird, then it has feathers. 2 angles are supplementary if they are a linear pair If 2 angles are a linear pair, then they are supplementary. HW: pg 82 #3-5HW pg. 82 #3­5, 7­15, 31 & 32 2
3. 3. 2.2 Conditional Statements September 01, 2011 • Conditional statements can be T or F. • Prove that the conclusion is true every time the hypothesis is true. • To show false: give 1 counterexample. Conditional Statement: If m A = 99, then A is obtuse. T Converse: exchange the hypothesis and conclusion If m A is obtuse, then m A = 99. F Inverse: negate both the hypothesis and conclusion If m A ≠99, then A is not obtuse. F Contrapositive: write the converse, then negate both hypothesis and conclusion T If A is not obtuse, then m A ≠ 99.HW pg. 82 #3­5, 7­15, 31 & 32 3
4. 4. 2.2 Conditional Statements September 01, 2011 HW: pg. 82 #3-5,7-15,31 & 32HW pg. 82 #3­5, 7­15, 31 & 32 4
5. 5. 2.2 Conditional Statements September 01, 2011 You can write a definition as a conditional statement in if-then form or as its converse. Both are True. Definition: If 2 lines intersect to form a right angle, then they are perpendicular lines. Converse: If 2 lines are perpendicular, then they intersect to form a right angle. You can write "line l is perpendicular to line m" as l m. l m HW pg. 83 #16-18HW pg. 82 #3­5, 7­15, 31 & 32 5
6. 6. 2.2 Conditional Statements September 01, 2011 Biconditional Statement: • When conditional statement and converse are T, then you can write them as a biconditional statement. • if and only if (IFF) • any valid definition can be written as biconditionalHW pg. 82 #3­5, 7­15, 31 & 32 6
7. 7. 2.2 Conditional Statements September 01, 2011HW pg. 82 #3­5, 7­15, 31 & 32 7
8. 8. 2.2 Conditional Statements September 01, 2011 HW pg.83 #16-25HW pg. 82 #3­5, 7­15, 31 & 32 8