Question

given: m || n and p is a transversal
prove: ( mangle2 = mangle7 )
what is the missing reason in the proof?

1. ( mparallel n ) and p is a transversal 1. given
2. ( angle2congangle3 ) 2. ver. ( angle s ) theorem
3. ( mangle2 = mangle3 ) 3. def. of congruent
4. ( angle3congangle7 ) 4. corr. ( angle s ) theorem
5. ( mangle3 = mangle7 ) 5. def. of congruent
6. ( mangle2 = mangle7 ) 6. ?

corresponding angles theorem
alternate interior angles theorem
transitive property
subtraction property

Explanation:

Step1: Analyze the given equalities

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

Step2: Apply the transitive property

The transitive property of equality 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