Question

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

statement	reason
2. ∠2 ≅ ∠3	2. def. of vert. ∠s
3. ∠2 ≅ ∠6	3. def. of corr. ∠s
4. ∠3 ≅ ∠6	4.

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

Explanation:

Step1: Recall Properties

We know from steps 2 and 3 that $\angle 2 \cong \angle 3$ and $\angle 2 \cong \angle 6$. We need to find the reason that $\angle 3 \cong \angle 6$.

Step2: Identify the Property

The transitive property of congruence states that if $a \cong b$ and $b \cong c$, then $a \cong c$. Here, let $a = \angle 3$, $b = \angle 2$, and $c = \angle 6$. Since $\angle 2 \cong \angle 3$ and $\angle 2 \cong \angle 6$, by transitive property, $\angle 3 \cong \angle 6$. The symmetric property is about if $a \cong b$ then $b \cong a$, which doesn't apply here. Vertical angles congruent was used in step 2, not step 4. Supplementary angles are about angles adding to 180°, which is not relevant here.

Answer:

transitive property