Question

what is the missing reason in the proof? (1 point) corresponding angles postulate transitive property of equality vertical angles theorem

Explanation:

Step1: Analyze each option

• Vertical Angles Theorem: This theorem is about vertical angles (opposite angles formed by two intersecting lines) being equal. But in the proof steps, there is no indication of vertical angles being used.
• Transitive Property of Equality: The transitive property states that if \(a = b\) and \(b = c\), then \(a = c\). This is not relevant to the substitution step in the given proof.
• Corresponding Angles Postulate: This postulate is about angles in corresponding positions when a transversal crosses parallel lines. But the key step here is substitution. In step 2, we have \(m\angle A=m\angle E\), and then in step 3, we substitute \(m\angle A\) with \(m\angle E\) in the equation \(m\angle A + m\angle C=180^{\circ}\) (from step 1) to get \(m\angle E + m\angle C = 180^{\circ}\).
• Vertical Angles Theorem: Again, not relevant to the substitution operation in the proof.

Answer:

Substitution (Since in step 3, we substitute \(m\angle A\) with \(m\angle E\) based on the equality \(m\angle A=m\angle E\) from step 2)