the figure shows a transversal that intersects two parallel lines. none of the angles are right angles…

the figure shows a transversal that intersects two parallel lines. none of the angles are right angles. which angles are congruent to ∠3? select all that apply. ∠1 ∠2 ∠4 ∠5 ∠6 ∠7 ∠8

the figure shows a transversal that intersects two parallel lines. none of the angles are right angles. which angles are congruent to ∠3? select all that apply. ∠1 ∠2 ∠4 ∠5 ∠6 ∠7 ∠8

Answer

Explanation:

Step1: Vertical angles

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

Step2: Corresponding angles

When two parallel lines are cut by a transversal, corresponding angles are congruent. $\angle3$ and $\angle7$ are corresponding angles. So $\angle3\cong\angle7$.

Step3: Alternate - interior angles

When two parallel lines are cut by a transversal, alternate - interior angles are congruent. $\angle3$ and $\angle5$ are alternate - interior angles (if we consider the parallel lines and the transversal). Wait, no. Let's re - check. Since $\angle1\cong\angle5$ (corresponding angles) and $\angle1\cong\angle3$ (vertical angles), then by the transitive property $\angle3\cong\angle5$.

Answer:

$\angle1$, $\angle5$, $\angle7$