Question

given: if a figure is a square, then all sides are congruent. figure abcd is a square. what conclusion can be drawn from the given statements and why? choose the correct answer. a) figure abcd has all sides congruent by the law of detachment. b) figure abcd has all sides congruent by the law of syllogism. c) figure abcd is a square by the law of detachment. d) no valid conclusion can be drawn. the given statements are not related in a way that allows either law to apply.

Explanation:

Step1: Recall Law of Detachment

The Law of Detachment states if \(p
ightarrow q\) is true and \(p\) is true, then \(q\) is true.

Step2: Identify \(p\) and \(q\)

Let \(p\) be "a figure is a square" and \(q\) be "all sides are congruent". Given \(p
ightarrow q\) is true and for figure \(ABCD\), \(p\) (figure \(ABCD\) is a square) is true.

Step3: Draw conclusion

By Law of Detachment, \(q\) is true for figure \(ABCD\), so figure \(ABCD\) has all sides congruent.

Answer:

A. Figure ABCD has all sides congruent by the Law of Detachment.