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 property

By the Same - Side Interior Angles Postulate, when two parallel lines are cut by a transversal, same - side interior angles are supplementary. Here, \(\angle3\) and \(\angle6\) are same - side interior angles.

Step2: Recall congruence of angles supplementary to the same angle

If two angles are supplementary to the same angle, they are congruent. Since \(\angle3\) and \(\angle6\) are supplementary to the same non - shown angle (the angle that forms a linear pair with both \(\angle3\) and \(\angle6\) in the context of parallel lines and transversal), they are congruent.

Step3: Analyze the relationship between \(\angle6\) and another angle

\(\angle6\) and \(\angle3\) are same - side interior angles. Also, \(\angle3\) and \(\angle6\) are supplementary to the same angle because of the linear pair relationships in the figure formed by the parallel lines \(l\) and \(m\) and the transversal \(t\).

Answer:

Since \(\angle3\) and \(\angle6\) are same - side interior angles, they are supplementary. Since \(\angle3\) and \(\angle6\) are supplementary to the same angle, they are congruent. \(\angle6\) and \(\angle3\) are same - side interior angles and supplementary to the same angle because of linear pair relationships in the figure with parallel lines \(l\) and \(m\) and transversal \(t\).