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

given: x // y and w is a transversal prove: ∠3 ≅ ∠6 what is the missing reason in the proof? statement reason 1. x // y w is a transversal 1. given 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

given: x // y and w is a transversal prove: ∠3 ≅ ∠6 what is the missing reason in the proof? statement reason 1. x // y w is a transversal 1. given 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

Answer

Explanation:

Step1: Analyze given congruences

We are given that $\angle2\cong\angle3$ (by definition of vertical - angles) and $\angle2\cong\angle6$ (by definition of corresponding angles).

Step2: Use transitive property

The transitive property of congruence states that if $a\cong b$ and $b\cong c$, then $a\cong c$. Here, $a = \angle3$, $b=\angle2$, and $c = \angle6$. Since $\angle3\cong\angle2$ and $\angle2\cong\angle6$, we can conclude that $\angle3\cong\angle6$ by the transitive property.

Answer:

transitive property