Question

given: m || n and p is a transversal
prove: m∠2 = m∠7
what is the missing reason in the proof?

1. m || n and p is a transversal - 1. given
2. ∠2 ≅ ∠3 - 2. ver. ∠s theorem
3. m∠2 = m∠3 - 3. def. of congruent
4. ∠3 ≅ ∠7 - 4. corr. ∠s theorem
5. m∠3 = m∠7 - 5. def. of congruent
6. m∠2 = m∠7 - 6.?

corresponding angles theorem
alternate interior angles theorem
transitive property
subtraction property

Explanation:

Step1: Recall the transitive property

The transitive property states that if \(a = b\) and \(b = c\), then \(a = c\).

Step2: Apply the transitive property

We have \(m\angle2=m\angle3\) (from step 3) and \(m\angle3 = m\angle7\) (from step 5).
By the transitive property, if \(m\angle2=m\angle3\) and \(m\angle3 = m\angle7\), then \(m\angle2=m\angle7\).

Answer:

transitive property