Question

complete the following plan to prove that ∠3 ≅ ∠6. use the same - side interior angles postulate to show that ∠3 is supplementary to ∠6. since ∠3 and ∠6 are to the same angle, they are congruent to each other. show ∠6 and ∠ are because they form 5 complementary supplementary congruent a linear pair a right angle vertical angles

Explanation:

Step1: Recall same - side interior angles

By the Same - Side Interior Angles Postulate, $\angle3$ and $\angle6$ are same - side interior angles.

Step2: Analyze supplementary relationship

Same - side interior angles are supplementary, so $\angle3+\angle6 = 180^{\circ}$.

Step3: Show congruence

Let $\angle3$ and $\angle6$ be supplementary to the same angle (say $\angle x$ such that $\angle3+\angle x=180^{\circ}$ and $\angle6+\angle x = 180^{\circ}$). Then, by the congruent supplements theorem (if two angles are supplementary to the same angle, they are congruent), $\angle3\cong\angle6$. Also, $\angle6$ and $\angle3$ are congruent because they are supplementary to the same angle.

Answer:

Same - side interior angles; the same angle; congruent supplements theorem; supplementary; congruent