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Explain Bot 1. The statement "if angles aren't congruent then they aren't equal in measure" is true. When angles are congruent, it means they have the same measure. Therefore, if angles are not congruent, it implies that their measures are different and thus not equal.
To understand this concept, you need to know the definition of congruent angles, which states that two angles are congruent if they have equal measures. The given statement is an example of a conditional statement, written in the form "If A, then B." In this case, A is "angles aren't congruent," and B is "they aren't equal in measure." The given statement says that if the antecedent (A) is true (angles aren't congruent), then the consequent (B) must also be true (they aren't equal in measure). Therefore, the statement is true.
2. No, the inverse and contrapositive of a conditional statement are not the same; they involve more than just switching the words.
The inverse of a conditional statement "If A, then B" is formed by negating both the antecedent (A) and the consequent (B) individually. So, the inverse of "If A, then B" will be "If not A, then not B." In other words, if the original statement is true, the inverse may or may not be true.
The contrapositive of a conditional statement "If A, then B" is formed by switching the positions of the antecedent (A) and the consequent (B) and then negating both of them. So, the contrapositive of "If A, then B" will be "If not B, then not A." The contrapositive is equivalent to the original statement in terms of truth value. If the original statement is true, the contrapositive will also be true, and if the original statement is false, the contrapositive will also be false.
Therefore, the inverse and contrapositive of a conditional statement are not the same; they have different forms but can have the same truth value.
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