Question

which of the following statements and justifications would prove that t // u? answer attempt 1 out of 3 ∠1≅∠5, by converse of corresponding angles ∠1≅∠4, by converse of same - side interior angles ∠1≅∠9, by converse of alternate exterior ∠1≅∠15, by converse of alternate exterior angles

Explanation:

Step1: Recall parallel - line determination theorems

The converse of corresponding - angles postulate states that if two lines are cut by a transversal and the corresponding angles are congruent, then the two lines are parallel. Corresponding angles are in the same relative position with respect to the transversal and the two lines.

Step2: Analyze each option

• For $\angle1\cong\angle5$: $\angle1$ and $\angle5$ are corresponding angles. According to the converse of corresponding - angles postulate, if $\angle1\cong\angle5$, then $t\parallel u$.
• For $\angle1\cong\angle4$: $\angle1$ and $\angle4$ are vertical angles, and the congruence of vertical angles does not prove that $t\parallel u$.
• For $\angle1\cong\angle9$: $\angle1$ and $\angle9$ are not in a special - angle relationship (such as corresponding, alternate interior, alternate exterior, or same - side interior) that can prove $t\parallel u$.
• For $\angle1\cong\angle15$: $\angle1$ and $\angle15$ are not in a special - angle relationship that can prove $t\parallel u$.

Answer:

$\angle1\cong\angle5$, by Converse of Corresponding Angles