Question

determine whether the conclusion is valid based on the given information. select valid or invalid. explain your reasoning.
given: right angles are congruent. ∠1 and ∠2 are right angles.
conclusion: ∠1 ≅ ∠2
valid
select choice
select choice
law of detachment
law of syllogism
m∠1 = m∠2 = 90°
need help?

Explanation:

The Law of Detachment states that if a conditional statement \(p
ightarrow q\) is true and \(p\) (the hypothesis) is true, then \(q\) (the conclusion) is true. Here, the general statement "Right angles are congruent" can be thought of as a conditional: if \(\angle x\) and \(\angle y\) are right - angles (\(p\)), then \(\angle x\cong\angle y\) (\(q\)). Since \(\angle1\) and \(\angle2\) are right - angles (\(p\) is true for \(\angle1\) and \(\angle2\)), by the Law of Detachment, \(\angle1\cong\angle2\) (\(q\) is true for \(\angle1\) and \(\angle2\)). Also, since \(m\angle1 = m\angle2=90^{\circ}\), by the definition of congruent angles (angles with equal measures are congruent), \(\angle1\cong\angle2\).

Answer:

valid, Law of Detachment, \(m\angle1 = m\angle2 = 90^{\circ}\)