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Cards In This Set
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If an animal is a beagle, then it is a dog.
What is the converse? |
If an animal is a dog, then it is a beagle.
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If an animal is a beagle, then it is a dog.
What is the inverse? |
If an animal isn't a beagle, then it isn't a dog.
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If an animal is a beagle, then it is a dog.
What is the contrapositive? |
If an animal isn't a dog, then it isn't a beagle.
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What words are always in the middle of a biconditional?
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If and only if
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What two statements must be true to write a biconditional?
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The conditional and its converse.
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Write the converse of "If the water is frozen, then the temperature is below 0oC"
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If the temperature is below 0oC then the water is frozen.
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Write the inverse of "If the water is frozen, then the temperature is below 0oC"
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If the water is NOT frozen, then the temperature is NOT below 0oC
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Write the contrapositive of "If the water is frozen, then the temperature is below 0oC"
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If the temperature is NOT below 0oC then the water is NOT frozen.
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Change to an "if-then" statement:
"Perpendicular lines form right angles." |
If lines are Perpendicular, then they form right angles
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Change to an "if-then" statement:
"Angles that form a linear pair are supplementary" |
If angles form a linear pair, then they are supplementary
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Convert the biconditional into 2 conditional statements that are converses of each other:
"Angles are complementary if and only if the sum of their measures is 90" |
If Angles are complementary, then the sum of their measures is 90. AND If the sum of the measures is 90, then the angles are complementary.
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Why isn't the definition below valid?
"If a polygon is a square, then it has 4 congruent angles" |
The converse is not true, If it has 4 right angles, it could be a square.
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Why is the definition below valid? "If a polygon is regular, then it is equilateral and equiangular"
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Because the converse is true, "If a polygon is equilateral and equiangular, then it is regular"
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What is a conjecture?
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A conclusion based on patterns
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Reasoning based on patterns or trends is called ___________.
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Inductive Reasoning
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