Question

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

Explanation:

Step1: Recall parallel - line theorems

Parallel lines can be proved by various angle - related converse theorems.

Step2: Analyze each option

• For alternate exterior angles, if two lines are cut by a transversal and alternate exterior angles are congruent, the lines are parallel. $\angle1$ and $\angle9$ are alternate exterior angles. If $\angle1\cong\angle9$, by the converse of alternate exterior angles, $t\parallel u$.
• For corresponding angles, if $\angle1\cong\angle5$, by the converse of corresponding angles, $t\parallel u$.
• For same - side interior angles, $\angle1$ and $\angle4$ are not same - side interior angles, so the statement “$\angle1\cong\angle4$, by converse of same - side interior angles” is incorrect.
• $\angle1$ and $\angle15$ are not alternate exterior angles.

Answer:

$\angle1\cong\angle9$, by Converse of Alternate Exterior Angles; $\angle1\cong\angle5$, by Converse of Corresponding Angles