Question

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

Explanation:

Step1: Recall linear - pair definition

A linear pair of angles are adjacent angles that form a straight - line. $\angle2$ and $\angle5$ are not adjacent and do not form a straight - line, so the statement “$\angle2$ and $\angle5$ form a linear pair” is false.

Step2: Recall vertical - angles property

Vertical angles are congruent. $\angle1$ and $\angle3$ are vertical angles, so $\angle3\cong\angle1$, and the statement “$\angle3\cong\angle1$” is true.

Step3: Recall corresponding - angles property for parallel lines

When two parallel lines are cut by a transversal, corresponding angles are congruent. $\angle4$ and $\angle8$ are corresponding angles, so $\angle4\cong\angle8$, and the statement “$\angle4\cong\angle8$” is true.

Step4: Recall same - side interior angles property for parallel lines

When two parallel lines are cut by a transversal, same - side interior angles are supplementary. $\angle3$ and $\angle8$ are not same - side interior angles, so the statement “$\angle3$ and $\angle8$ are supplementary” is false.

Step5: Recall alternate exterior angles property for parallel lines

When two parallel lines are cut by a transversal, alternate exterior angles are congruent. $\angle6$ and $\angle1$ are alternate exterior angles, so $\angle6\cong\angle1$, and the statement “$\angle6\cong\angle1$” is true.

Answer:

$\angle3\cong\angle1$, $\angle4\cong\angle8$, $\angle6\cong\angle1$