Question

given: ( x parallel y ) and ( w ) is a transversal
prove: ( angle 3 cong angle 6 )
what is the missing reason in the proof?

1. ( x parallel y )

( w ) is a transversal

1. given
2. ( angle 2 cong angle 3 )
3. def. of vert. ( angle s )
4. ( angle 2 cong angle 6 )
5. def. of corr. ( angle s )
6. ( angle 3 cong angle 6 )

4.
transitive property
symmetric property
vertical angles are congruent
definition of supplementary angles

Explanation:

Step1: Recall properties of congruent angles

We know that if \(a\cong b\) and \(b\cong c\), then \(a\cong c\) by the transitive property of congruence.
In this proof, we have \(\angle2\cong\angle3\) (from the definition of vertical angles) and \(\angle2\cong\angle6\) (from the definition of corresponding angles).

Step2: Apply the transitive property

Since \(\angle3\) and \(\angle6\) are both congruent to \(\angle2\), we can say \(\angle3\cong\angle6\) using the transitive property.

Answer:

transitive property