Section 2-2 Biconditionals and Definitions. What is a biconditional When both the conditional and converse are true the statement can be written as: If.

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Presentation transcript:

Section 2-2 Biconditionals and Definitions

What is a biconditional When both the conditional and converse are true the statement can be written as: If and only if

Example If the Pistons are the best team in basketball, then they will win the NBA championship If the Pistons win the NBA championship, then they are the best team in basketball Both the conditional and the converse are true so the statement can be written as a biconditional The Pistons are the best team in basketball if and only if they win the NBA championship.

Try on your own Can you turn the following statement into a biconditional: Conditional: If two lines are perpendicular, then they intersect to form right angles. Converse: If two lines intersect to form right angles, then they are perpendicular Remember to leave out If and then from the hypothesis and conclusion Answer is on the next slide

Answer Is the conditional true? – Yes Is the converse true? – Yes Conditional: If two lines are perpendicular, then they intersect to form right angles. (Hypothesis)____________________ if and only if (Conclusion)___________________ The biconditional is: Two lines are perpendicular if and only if they intersect to form right angles.

Time to read Top of page 89 in your geometry book.

What makes a good definition? A good definition should be reversible Example: A triangle is a three sided polygon Bad Example: An airplane is a vehicle that flies – A helicopter also flies

Quick Check #3 Statement: A right angle is an angle whose measure is 90 degrees Conditional: If an angle is a right angle, then the measure is 90 degrees Converse: If an angle has a measure of 90 degrees, then it’s a right angle Could you create a biconditional? Yes Good Definition?

Problem #2 If x = 12, then 2x – 5 = 19 Converse: If 2x – 5 = 19, then x = 12 Are they both true? Yes x = 12 if and only if 2x – 5 = 19

Problem #16 A rectangle is a four sided figure with at least one right angle. Is the converse true? No, the converse is not true because there could be a four sided figure with one right angle, that is not a rectangle