Question

which of the following statements and justifications would prove that t // u? answer attempt 2 out of 2 ∠1=∠7, by converse of alternate exterior angles ∠7 and ∠10 are supplementary, by converse of same - side interior angles ∠3 and ∠8 are supplementary, by converse of same - side interior angles ∠7 and ∠8 are supplementary, by converse of linear pairs

Explanation:

Step1: Recall parallel - line theorems

The converse of alternate - exterior angles states that if two alternate - exterior angles are congruent, then the two lines are parallel. $\angle1$ and $\angle7$ are alternate - exterior angles. If $\angle1=\angle7$, then $t\parallel u$.

Step2: Analyze other options

• For $\angle3$ and $\angle8$, they are same - side interior angles for lines $r$ and $s$, not for $t$ and $u$.
• For $\angle7$ and $\angle10$, they are not related in a way that can prove $t\parallel u$ using common parallel - line theorems.
• For $\angle7$ and $\angle8$, they are a linear pair, and the converse of linear pairs is not used to prove parallel lines.

Answer:

$\angle1 = \angle7$, by Converse of Alternate Exterior Angles