Question

given: m || n and p is a transversal
prove: m∠2 = m∠7

diagram of lines m, n (parallel), transversal p with angles 1,2,3,4 on line m; angles 5,6,7,8 on line n

what is the missing reason in the proof?

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

options:

• corresponding angles theorem
• alternate interior angles theorem
• transitive property
• subtraction property

Explanation:

Step1: Recall the transitive property

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

Step2: Apply to the given angles

From step 3, we have \( m\angle2 = m\angle3 \), and from step 5, we have \( m\angle3 = m\angle7 \). Using the transitive property, we can conclude that \( m\angle2 = m\angle7 \).

Answer:

transitive property