Question

Use the premises and conclusion to answer the questions.

Premises:
If a quadrilateral has two pairs of parallel sides, then it is a parallelogram.
If a quadrilateral is a parallelogram, then its opposite angles are congruent.

Conclusion:
If a quadrilateral has two pairs of parallel sides, then its opposite angles are congruent.



Which statement best describes this argument?

The argument is valid by the law of syllogism.

The argument is invalid because the conclusion does not follow the premises.

The argument is valid by the law of detachment.

The argument is invalid because the premises are not true.

Answer 1

The argument is valid by the law of syllogism.

Explanation:

The law of syllogism is also called the law of transitivity. It is based on the transitive property, which states "if a = b and b = c, then a = c."

In our problem, our statement a would be "A quadrilateral has two pairs of parallel sides". Our statement b would be "It is a parallelogram." Our statement c would be "Its opposite angles are congruent."

That would make "if a = b"

"If a quadrilateral has two pairs of parallel sides it is a parallelogram."

Then "b = c" would be

"If a quadrilateral is a parallelogram, its opposite angles are congruent."

"a = c" would then be

"If a quadrilateral has two pairs of parallel sides its opposite angles are congruent."

This is the conclusion we were given, so this is the law of syllogism.