Question

given ( xparallel y ) and ( w ) is a transversal
prove ( angle 3congangle 6 )
what is the missing reason in the proof?

1. ( xparallel y ) and ( w ) is a transversal
2. given
3. ( angle 2congangle 3 )
4. def. of vert. ( angle )s
5. ( angle 2congangle 6 )
6. def. of corr. ( angle )s
7. ( angle 3congangle 6 )
8. ?

symmetric property
transitive property

Explanation:

Step1: Recall the transitive property of congruence

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

Step2: Apply the property to the angles

We know \(\angle2\cong\angle3\) (from step 2) and \(\angle2\cong\angle6\) (from step 3). Let \(a = \angle3\), \(b=\angle2\), and \(c = \angle6\). By the transitive property, since \(\angle3\cong\angle2\) and \(\angle2\cong\angle6\), we can conclude \(\angle3\cong\angle6\).

Answer:

transitive property