Question

the figure shows a pair of parallel lines cut by a transversal. which three angles are congruent to ∠2? choose all three correct angles. ∠3 ∠4 ∠5 ∠6 ∠7 ∠8

Explanation:

Step1: Identify vertical - angle relationship

Vertical angles are congruent. $\angle2$ and $\angle3$ are vertical angles, so $\angle2\cong\angle3$.

Step2: Identify corresponding - angle relationship

Corresponding angles formed by parallel lines and a transversal are congruent. $\angle2$ and $\angle6$ are corresponding angles, so $\angle2\cong\angle6$.

Step3: Identify alternate - interior - angle relationship

$\angle2$ and $\angle7$ are alternate - interior angles. For parallel lines cut by a transversal, alternate - interior angles are congruent, so $\angle2\cong\angle7$.

Answer:

$\angle3$, $\angle6$, $\angle7$