Question

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

statement	reason
2. ( angle2 cong angle3 )	2. ver. ( angle s ) theorem
3. ( mangle2 = mangle3 )	3. def. of congruent
4. ( angle3 cong angle7 )	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:

We know that \( m\angle2 = m\angle3 \) (from step 3) and \( m\angle3 = m\angle7 \) (from step 5). The transitive property of equality states that if \( a = b \) and \( b = c \), then \( a = c \). Here, \( a = m\angle2 \), \( b = m\angle3 \), and \( c = m\angle7 \), so we use the transitive property to conclude \( m\angle2 = m\angle7 \). The other options don't fit: corresponding angles theorem relates to parallel lines and transversals for specific angle pairs (not for equality transitivity), alternate interior angles theorem is also about parallel lines and specific angle pairs, and subtraction property is about subtracting equal quantities, which isn't the case here.

Answer:

transitive property