Write the contrapositive of the statement below.

If a triangle is an obtuse triangle, then it has one angle with measure greater than 90°

A triangle has one angle greater than 90°.

A triangle is an obtuse triangle.

If a triangle is not an obtuse triangle, then it does not have one angle greater than 90°.

If a triangle does not have one angle greater than 90°, then it is not an obtuse triangle.

Question

Mathematics

Carla

9 May, 09:24

Write the contrapositive of the statement below.

If a triangle is an obtuse triangle, then it has one angle with measure greater than 90°

A triangle has one angle greater than 90°.

A triangle is an obtuse triangle.

If a triangle is not an obtuse triangle, then it does not have one angle greater than 90°.

If a triangle does not have one angle greater than 90°, then it is not an obtuse triangle.

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Answers (1)

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Ramiro Walter · Answer 1

If a triangle does not have one angle greater than 90Â°, then it is not an obtuse triangle. Remember that you create a contrapositive by inverting and swapping both terms. So if you have if A then B the contrapositive would be if not-B then not-A Since you've been given "If a triangle is an obtuse triangle, then it has one angle with measure greater than 90Â°" the contrapositive would be something like "If a triangle has no angles with a measure greater than 90Â°, then it is not an obtuse triangle." So, now look at the available choices and see what matches in intent even if it's not phrased exactly the same. The option "If a triangle does not have one angle greater than 90Â°, then it is not an obtuse triangle." matches the intent of the contrapositive that we constructed independently and is the correct answer.