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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
