Answer: Choice B)
If corresponding angles are not congruent, then the lines are not parallel.
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Explanation:
The given conditional is in the form "If P, then Q"
where,
- P = two lines are parallel
- Q = corresponding angles are congruent
The P and Q are placeholders for those definitions shown above. So we'll simply do a "search and replace" to replace P and Q with those phrases. We do this shortening so that we can do logical operations.
Specifically, we'll do two things:
- Swap the positions of P and Q
- Place a "not" before each letter after the swap
We go from the format "if P, then Q" to "if not Q, then not P". Those two formats are equivalent in truth value. This is known as the contrapositive.
In terms of the problem at hand, the phrase "if not Q, then not P" becomes "If corresponding angles are not congruent, then the lines are not parallel"
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In short, we swap each part of the original "if ..., then ..." statement, and stick "not"s in there to negate each piece.
