Question

complete the following plan to prove that ∠3 ≅ ∠6.
drag and drop an answer choice into each empty box below, or use keyboard navigation. tab to navigate, space to select, arrow keys to move between panes. enter to place.
5 complementary supplementary congruent a linear pair a right angle vertical angles
use the same-side interior angles postulate to show that ∠3 is supplementary to ∠
show ∠6 and ∠
are
because they form
since ∠3 and ∠6 are

the same angle, they are congruent to each other.

Explanation:

Step1: Use Same - Side Interior Angles Postulate

By the Same - Side Interior Angles Postulate, if two parallel lines \( l\) and \( m\) are cut by a transversal \( t\), then \(\angle3\) and \(\angle6\) are same - side interior angles. And \(\angle3\) is supplementary to \(\angle6\) (because for same - side interior angles formed by parallel lines and a transversal, they are supplementary), so we can say \(\angle3+\angle6 = 180^{\circ}\).

Step2: Analyze the relationship of \(\angle6\) and another angle

\(\angle6\) and \(\angle5\) are a linear pair (since they are adjacent angles that form a straight line along the transversal \( t\) and one of the parallel lines \( m\)). By the definition of a linear pair, \(\angle6+\angle5=180^{\circ}\).

Step3: Use the property of supplementary angles

Since \(\angle3+\angle6 = 180^{\circ}\) (from Step1) and \(\angle6+\angle5 = 180^{\circ}\) (from Step2), by the property that if \(a + b=c + b\), then \(a = c\) (subtracting \(b\) from both sides of the equations), we can conclude that \(\angle3\cong\angle5\) (because they are both supplementary to \(\angle6\)). Also, \(\angle5\) and \(\angle6\) form a linear pair.

Answer:

First blank: \(6\); Second blank: \(5\); Third blank: a linear pair