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. ?

Explanation:

Step1: Analyze the given statements

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

Step2: Apply the transitive property

If \(a = b\) and \(b = c\), then \(a = c\). Here, \(a=m\angle2\), \(b = m\angle3\), and \(c=m\angle7\).

Answer:

transitive property of equality