Question

given: x || y and w is a transversal
prove: ∠3 ≅ ∠6
what is the missing reason in the proof?

1. x || y
2. given
3. ∠2 ≅ ∠3
4. def. of vert. ∠s
5. ∠2 ≅ ∠6
6. def. of corr. ∠s
7. ∠3 ≅ ∠6

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

Explanation:

Step1: Recall vertical angles property

Vertical angles are congruent. So, $\angle2\cong\angle3$ (by definition of vertical angles).

Step2: Use parallel - line and transversal property

Since $x\parallel y$ and $w$ is a transversal, by the definition of corresponding angles, $\angle2\cong\angle6$.

Step3: Apply transitive property

If $\angle2\cong\angle3$ and $\angle2\cong\angle6$, then by the transitive property of congruence (if $a = b$ and $a = c$, then $b = c$), $\angle3\cong\angle6$.

Answer:

transitive property