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 invalid because the conclusion does not follow the premises.
the argument is invalid because the premises are not true.
the argument is valid by the law of syllogism.
the argument is valid by the law of detachment.

Explanation:

Step1: Recall the law of syllogism

The law of syllogism states that if \(p
ightarrow q\) and \(q
ightarrow r\), then \(p
ightarrow r\).
Let \(p\) be “a quadrilateral has two pairs of parallel sides”, \(q\) be “it is a parallelogram” and \(r\) be “its opposite angles are congruent”.
The first premise is \(p
ightarrow q\) (If a quadrilateral has two pairs of parallel sides, then it is a parallelogram) and the second premise (implied from the properties of parallelograms) is \(q
ightarrow r\) (If a quadrilateral is a parallelogram, then its opposite angles are congruent).

Step2: Apply the law of syllogism

By the law of syllogism, since \(p
ightarrow q\) and \(q
ightarrow r\), we can conclude \(p
ightarrow r\) (If a quadrilateral has two pairs of parallel sides, then its opposite angles are congruent)

Answer:

The argument is valid by the law of syllogism.