Question

determine if s || t. state which postulate or theorem you would use to prove they are or are not parallel.
7.
9.
6.
8.

Explanation:

Step1: Recall parallel - line postulates

If corresponding angles are congruent, alternate - interior angles are congruent, or same - side interior angles are supplementary, then the lines are parallel.

Step2: Analyze figure 6

The two 87 - degree angles are corresponding angles. Since they are congruent ($87^{\circ}=87^{\circ}$), by the corresponding - angles postulate, $s\parallel t$.

Step3: Analyze figure 7

The 89 - degree and 91 - degree angles are same - side interior angles. Their sum is $89 + 91=180^{\circ}$. By the same - side interior angles postulate, $s\parallel t$.

Step4: Analyze figure 8

The 75 - degree and 105 - degree angles are same - side interior angles. Their sum is $75 + 105 = 180^{\circ}$. By the same - side interior angles postulate, $s\parallel t$.

Step5: Analyze figure 9

The 60 - degree and 120 - degree angles are same - side interior angles. Their sum is $60+120 = 180^{\circ}$. By the same - side interior angles postulate, $s\parallel t$.

Answer:

In figure 6, $s\parallel t$ (by corresponding - angles postulate). In figure 7, $s\parallel t$ (by same - side interior angles postulate). In figure 8, $s\parallel t$ (by same - side interior angles postulate). In figure 9, $s\parallel t$ (by same - side interior angles postulate).