Question

parallel lines h and g are cut by transversal t. which statements are true? select all that are correct. ∠4≅∠8 ∠3≅∠1 ∠2 and ∠5 form a linear pair. ∠6≅∠1 ∠3 and ∠8 are supplementary.

Explanation:

Step1: Recall corresponding - angles property

When parallel lines are cut by a transversal, corresponding angles are congruent. $\angle4$ and $\angle8$ are corresponding angles, so $\angle4\cong\angle8$.

Step2: Recall vertical - angles property

Vertical angles are congruent. $\angle3$ and $\angle1$ are vertical angles, so $\angle3\cong\angle1$.

Step3: Recall linear - pair definition

A linear pair of angles are adjacent and supplementary. $\angle2$ and $\angle5$ are not adjacent, so they do not form a linear pair.

Step4: Recall alternate - exterior - angles property

$\angle6$ and $\angle1$ are alternate - exterior angles. When parallel lines are cut by a transversal, alternate - exterior angles are congruent, so $\angle6\cong\angle1$.

Step5: Recall same - side interior - angles property

$\angle3$ and $\angle8$ are same - side interior angles. When parallel lines are cut by a transversal, same - side interior angles are supplementary, so $\angle3$ and $\angle8$ are supplementary.

Answer:

$\angle4\cong\angle8$, $\angle3\cong\angle1$, $\angle6\cong\angle1$, $\angle3$ and $\angle8$ are supplementary.