If ∠1 and ∠2 are vertical angles, then m∠1 = m∠2.We are asked to state the law of logic that is illustrated in this exercise. To do so, we will start by recalling the Law of Syllogism.
&1. If hypothesis p, then conclusion q. [0.5em]
&2. If hypothesis q, then conclusion r.
&3. If hypothesis p, then conclusion r.
According to this law, if the first and the second statements are true, then the third statement is true. Let's analyze the given conditional statements and color-code the different hypotheses and conclusions that have been stated.
&1. If ∠1 and ∠2 are vertical angles, then ∠1≅ ∠2. [0.5em]
&2. If ∠1≅ ∠2, then m∠1= m∠2. [0.2em]
&3. If ∠1 and ∠2 are vertical angles, then m∠1 = m∠2.
Notice that the hypothesis of the second conditional statement matches the conclusion of the first conditional statement. This means that we can use the Law of Syllogism to write the third conditional statement. Therefore, the exercise illustrates the Law of Syllogism.
