Question

given: ( m parallel n ) and ( p ) is a transversal
prove: ( m angle 2 = m angle 7 )
what is the missing reason in the proof?

statement	reason
2. ( angle 2 cong angle 3 )	2. ver. ( angle )s theorem
3. ( m angle 2 = m angle 3 )	3. def. of congruent
4. ( angle 3 cong angle 7 )	4. corr. ( angle )s theorem
5. ( m angle 3 = m angle 7 )	5. def. of congruent
6. ( m angle 2 = m angle 7 )	6. ?

corresponding angles theorem
alternate interior angles theorem
transitive property
subtraction property

Explanation:

Step1: Analyze the given equalities

We know \(m\angle2 = m\angle3\) (from step 3) and \(m\angle3 = m\angle7\) (from step 5).

Step2: Apply the transitive property

The transitive property states that if \(a = b\) and \(b = c\), then \(a = c\). Here, \(a=m\angle2\), \(b = m\angle3\), and \(c=m\angle7\).

Answer:

transitive property