Use the conditional statement to answer the question. If an angle is a right angle, then the angle measures 90°. Are the stateme

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Use the conditional statement to answer the question. If an angle is a right angle, then the angle measures 90°. Are the stateme

nt and its contrapositive true? The statement is true, but the contrapositive is false. Both the statement and its contrapositive are false. The statement is false, but the contrapositive is true. Both the statement and its contrapositive are true.

Mathematics

2 answers:

SVEN [57.7K] · Answer 1 · 2022-05-22T11:05:14+03:00

To answer this question, we need a strong understanding of what "contrapositive" means:
The contrapositive of a conditional statement flips the hypothesis and conclusion, and makes both negative.
Here is an example:
Conditional Statement: If I am sick, then I stay home from school.
Hypothesis: I am sick, Conclusion: I stay home from school
Contrapositive: If I do not stay home from school, I am not sick.

What would be the contrapositive in our conditional statement?
Conditional Statement: <span>If an angle is a right angle, then the angle measures 90°
Contrapositive: If the angle does not measure 90</span>°, then the angle is not a right angle.
In this case, both the conditional statement and the contrapositive are true. We know this because a 90° angle and a right angle are the same thing.