Question

statements

1. ( nmparallel po )
2. ( angle 2=angle 3 )
3. ( angle 1=angle 3 )
4. ( angle 1=angle 2 )
5. ( lmparallel no )

reasons

1. given
2. alternate interior angles theorem
3. given

?

1. converse of alternate interior angles theorem

what is the missing reason in the proof?
( \bigcirc ) given
( \bigcirc ) transitive property
( \bigcirc ) alternate interior angles theorem
( \bigcirc ) converse alternate interior angles theorem

Explanation:

Step1: Analyze the relationship between angles

From statement 2 ($\angle2=\angle3$) and statement 3 ($\angle1 = \angle3$), we can use the transitive property. If $\angle2=\angle3$ and $\angle1=\angle3$, then $\angle1=\angle2$ (by transitive property of equality for angles).

Step2: Relate to parallel lines

When $\angle1=\angle2$, these are alternate interior angles. According to the converse of the alternate - interior angles theorem, if alternate interior angles are equal, then the lines are parallel. Here, $\angle1$ and $\angle2$ are alternate interior angles for lines $LM$ and $NO$ with a transversal (not shown in the problem but implied in angle - line relationships).

Answer:

converse alternate interior angles theorem