Do Now: 1.Copy Down HW. 2.Describe the pattern, then find the next two numbers in the pattern: 3, 12, 48, 192, …

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Do Now: 1.Copy Down HW. 2.Describe the pattern, then find the next two numbers in the pattern: 3, 12, 48, 192, …

2.2 Conditional Statements 5 cards

Conditional Statements: A fact written as “If, Then” If = Hypothesis Then = Conclusion

Ex 1: Identify the Hypothesis and the Conclusion If Varsity wins the game, then they go to the finals. If two lines are parallel, then the lines are coplanar. If x – 6 = 4, then x = 10

Ex 1: Identify the Hypothesis and the Conclusion If Varsity wins the game, then they go to the finals. If two lines are parallel, then the lines are coplanar. If x – 6 = 4, then x = 10

Ex 2: Write a Conditional An acute angle measures less than 90 degrees. If an angle is acute, then it measures less than 90 degrees. An Integer that ends with 0 is divisible by 5. If an integer ends with 0, then it is divisible by 5 A square has four congruent sides. If a figure is a square, then it has four congruent sides.

Truth Value True means ALWAYS true. False means FALSE at least ONCE.

Ex 3: False Conditionals: Give at lease one counterexample to prove the statements false. If you are a girl, then you have long hair. If it is February, then there are only 28 days in the month. If x squared is greater than 0, then x is greater than 0.

Converse Switch Hypothesis and Conclusion NOT ALWAYS TRUE

Ex 4: Converse ; Switch Hypothesis and Conclusion NOT ALWAYS TRUE Conditional: If two lines are parallel, then they never intersect. Converse: If two lines never intersect, then they are parallel True or False? FALSE: They could be skew

Converse : Switch Hypothesis and Conclusion NOT ALWAYS TRUE Conditional: If an angle measures 90 degrees, then it is a right angle. Converse: If an angle is a right angle, then it measures 90 degrees. True or False?

Converse : Switch Hypothesis and Conclusion NOT ALWAYS TRUE Conditional: If an angle measures 90 degrees, then it is a right angle. Converse: If an angle is a right angle, then it measures 90 degrees. True

Write the Converse, Determine if the converse is True or False. Conditional: If x = 9, then x + 3 = 12. Converse: If x + 3 = 12, then x = 9. True

Summary Conditional: If a is true, then b is true. Read it “If A, then B” A B Converse: Switch A and B; Not always true B A

Inverse Negate the Hypothesis and Conclusion NOT ALWAYS TRUE

Example 5: Write the inverse, Determine if the inverse is True or False. Conditional: If an animal is a whale, then it is a mammal. Inverse: If an animal is not a whale, then it is not a mammal. False Conditional: If an animal is a whale, then it is a mammal. Inverse: If an animal is not a whale, then it is not a mammal. False

Write the inverse, Determine if the inverse is True or False. Conditional: If a polygon is regular, then the polygon is equilateral. Inverse: If a polygon is not regular, then the polygon is not equilateral. False Conditional: If a polygon is regular, then the polygon is equilateral. Inverse: If a polygon is not regular, then the polygon is not equilateral. False

Contrapositive Negate the Hypothesis and Conclusion then Switch Them NOT ALWAYS TRUE

Example 6: Write the Contrapositive, Determine if the contrapositive is True or False. Conditional: If you are on the Varsity Football Team, then you wear a football jersey. Contrapositive: If you don’t wear a football jersey, then you are not on the Varsity Football Team.

Write the Contrapositive, Determine if the contrapositive is True or False. Conditional: If a figure is a square, then it has four right angles. Contrapositive: If a figure does not have four right angles, then the figure is not a square. True

Bi-conditional If a conditional and its converse are true, then the statement can be written as “if and only if.”

Write the Bi-Conditional Conditional: If a number is divisible by 2, then it is even. Converse: If a number is even, then it is divisible by 2. True Bi-Conditional: A number is divisible by 2 if and only if it is even.

Exit Slip: Write an if, then statement that is true. Then write the converse, inverse, and contrapositive of that statement-tell whether each of those statements are true or false.