Question

Which statement is logically equivalent to the following statement?

Answer 1

Answer:

Contrapositive: If a triangle does not have two acute angles, then it does not have one right angle.

Step-by-step explanation:

The statement: If a triangle has one right angle, the triangle has two acute angles.

"If" portion, or hypothesis: one right angle

"Then" portion, or conclusion: two acute angles

Converse structure: If conclusion, then hypothesis

Contrapositive structure: If negative conclusion, then negative hypothesis

Inverse structure: If negative hypothesis, the negative conclusion

Converse: If a triangle has two acute angles, then the triangle has one right angle.

--> This is is false because if a triangle has two acute angles, the third angle could also be acute or obtuse, not necessarily right.

Contrapositive: If a triangle does not have two acute angles, then it does not have one right angle.

--> This is true. If a triangle has two angles which are not both acute, the third angle cannot be right.

(The three angles total to 180°. For a triangle to have a right angle, the other two angles will add to 90°, each angle being less than 90°, making them acute).

Inverse: If a triangle does not have one right angle, then the triangle does not have two acute angles.

--> This is false. If a triangle does not have one right angle, it could have an obtuse angle and still have two acute angles.