Transcript 2-2 Biconditionals and Definitions

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When conditional and converse are true
Connectecd by “if and only if”
◦ Symbol is iff
Conditional
◦ If two angles have the same measure, then the angles are
congruent.
◦ Decide if T or F
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Converse
◦ If two angles are congruent, the angles have the same measure.
◦ Decide if T or F
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If both T, then write a biconditional.
◦ Must follow conditional pattern
◦ No if, then statement
 Two angles have the same measure if and only if the angles are
congruent.
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Conditional
◦ If three points are collinear, then they lie on the same line.
◦ T or F
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Converse
◦ If three points lie on the same line, then they are collinear.
◦ T or F
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Bicond.
◦ Three points are collinear if and only if they lie on the same line.
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Symbolically p ↔ q reads p if and only if q
Write cond and conv from bicond.
A number is divisible by 3 if and only if the sum of the digits
is divisible by 3.
Conditional
◦ If a number is divisible by 3, then the sum of the digits is divisible by 3.
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Converse
◦ If the sum of the digits of a number is divisible by 3, then the number is
divisible by 3.
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Bicond.
◦ A number is prime if and only if it has only two distinct factors, 1 and
itself.
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Conditional
◦ If a number is prime, then it has only two distinct factors, 1 and itself.
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Converse
◦ If a number has only two distinct factors, 1 and itself, then it is a prime
number.
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Good definitions identify or classify and object
Several important components
◦ Clearly understood terms
 Commonly understood or already defined
◦ Precise
 Avoid words like large, sort of, almost
◦ Reversible
 Can write as a biconditional
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Write as an biconditional
◦ Two lines are perpendicular if and only if they intersect to form right
angles.